Fractal Quotes

The truth is you already know what it's like. You already know the difference between the size and speed of everything that flashes through you and the tiny inadequate bit of it all you can ever let anyone know. As though inside you is this enormous room full of what seems like everything in the whole universe at one time or another and yet the only parts that get out have to somehow squeeze out through one of those tiny keyholes you see under the knob in older doors. As if we are all trying to see each other through these tiny keyholes. But it does have a knob, the door can open. But not in the way you think...The truth is you've already heard this. That this is what it's like. That it's what makes room for the universes inside you, all the endless inbent fractals of connection and symphonies of different voices, the infinities you can never show another soul. And you think it makes you a fraud, the tiny fraction anyone else ever sees? Of course you're a fraud, of course what people see is never you. And of course you know this, and of course you try to manage what part they see if you know it's only a part. Who wouldn't? It's called free will, Sherlock. But at the same time it's why it feels so good to break down and cry in front of others, or to laugh, or speak in tongues, or chant in Bengali--it's not English anymore, it's not getting squeezed through any hole. So cry all you want, I won't tell anybody.

Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.

Kisses were not supposed to be like this. Kisses were to be witnessed by stars, not held in the presence of stale death. But as the bones rose around them, Laila saw fractals of white. They looked like pale constellations, and she thought that, perhaps, for a kiss like this, even hell would put forth stars.

Evolution has no foresight. Complex machinery develops its own agendas. Brains — cheat. Feedback loops evolve to promote stable heartbeats and then stumble upon the temptation of rhythm and music. The rush evoked by fractal imagery, the algorithms used for habitat selection, metastasize into art. Thrills that once had to be earned in increments of fitness can now be had from pointless introspection. Aesthetics rise unbidden from a trillion dopamine receptors, and the system moves beyond modeling the organism. It begins to model the very process of modeling. It consumes evermore computational resources, bogs itself down with endless recursion and irrelevant simulations. Like the parasitic DNA that accretes in every natural genome, it persists and proliferates and produces nothing but itself. Metaprocesses bloom like cancer, and awaken, and call themselves I.

If reality is not what you want it to be, change it.

I believe that scientific knowledge has fractal properties, that no matter how much we learn, whatever is left, however small it may seem, is just as infinitely complex as the whole was to start with. That, I think, is the secret of the Universe.

Every you, every me. Fractals. Fractures.

You existed. You existed now as a fractal. Definition: A fractal is generally a rough or fragmented geometric shape that can be broken into parts, each of which is (at least approximately) a reduced-size copy of the whole. Maybe I was a fractal. Maybe the photographer was a fractal. Maybe we were all fractals.

It's not so much that history is simply cyclical, it seems to progress via recursive, repeated fractal patterns with minute variations.

My life seemed to be a series of events and accidents. Yet when I look back, I see a pattern.

In a fractal conception, I am a cell-sized unit of the human organism, and I have to use my life to leverage a shift in the system by how I am, as much as with the things I do. This means actually being in my life, and it means bringing my values into my daily decision making. Each day should be lived on purpose.

Maybe relationships could have fractals, too. And maybe the sense of loss was when you're becoming a fractal of what you once were to each other.

It is now known to science that there are many more dimensions than the classical four. Scientists say that these don’t normally impinge on the world because the extra dimensions are very small and curve in on themselves, and that since reality is fractal most of it is tucked inside itself. This means either that the universe is more full of wonders than we can hope to understand or, more probably, that scientists make things up as they go along.

Being who you are for ever is the price you pay for im­mor­tal­ity.

IN THE MIND’S EYE, a fractal is a way of seeing infinity.

Live on berries in a hollowed-out comet lit by artificial suns long enough, and you start to have delusions about achieving enlightenment.

Fractal litigation, whereby the flapping of a butterfly’s wings on one side of the world resulted in a massive compensation claim on the other.

Nature forms patterns. Some are orderly in space but disorderly in time, others orderly in time but disorderly in space. Some patterns are fractal, exhibiting structures self-similar in scale. Others give rise to steady states or oscillating ones. Pattern formation has become a branch of physics and of materials science, allowing scientists to model the aggregation of particles into clusters, the fractured spread of electrical discharges, and the growth of crystals in ice and metal alloys. The dynamics seem so basic—shapes changing in space and time—yet only now are the tools available to understand them.

Will you respond, establishing complicity, continuing our self-destructive paper trail, just to get in the last word? Will you cut off, leaving my note to spin its fractal math inside you? I wonder which I’d rather.

Consider cotton prices," Malcolm said. "There are good records of cotton prices going back more than a hundred years. When you study fluctuations in cotton prices, you find that the graph of price fluctuations in the course of a day looks basically like the graph for a week, which looks basically like the graph for a year, or for ten years. And that's how things are. A day is like a whole life. You start out doing one thing, but end up doing something else, plan to run an errand, but never get there... And at the end of your life, your whole existence has that same haphazard quality, too. Your whole life has the same shape as a single day.

(Since algebra derives from the Arabic jabara = to bind together, fractal and algebra are etymological opposites!)

How can unity and infinity share the same space? There is only one way, as a fractal.

Later, he was to decide that Andrew’s life had been fractally weird. That is, you could take any small piece of it and examine it in detail and it, in and of itself, would turn out to be just as complicated and weird as the whole thing in its entirety.

I’m not much of a chess player, but there is an aspect of the game that I find fascinating. After a while, you can almost see lines of force between the pieces. Areas of danger where it is physically impossible to move pieces into. Clouds of possibility, forbidden zones.

this garden is your soul. This mess is you! Together, you and I, we have been working with a purpose in your heart. And it is wild and beautiful and perfectly in process. To you it seems like a mess, but I see a perfect pattern emerging and growing and alive—a living fractal.

What is inevitable is not death but change. Change is the only abiding reality. The metaverse evolves, fractally and forever. Saints become sinners, sinners become saints. Dust becomes men, men become gods, gods become dust.

At other times I wake up from the half sleep I'd fallen into, and hazy images with poetical and unpredictable colours play out their silent show to my inattention.

It feels like trying to juggle eight-side Rubik’s cubes while trying to solve them at the same time. And every time I drop one, God kills a billion kittens.

The natural world is built upon common motifs and patterns. Recognizing patterns in nature creates a map for locating yourself in change, and anticipation what is yet to come.

The unfolding over time of a great idea is like the growth of a fractal crystal, allowing details and refinements to multiply endlessly — but only in ever-increasing scale.

The past is fractal premonition, infinite to the eye but nothing to be built on . . .

What are you thinking, Evan?" So I told him. Every you, every me. Fractals. Fracturs. "I wonder who she is now," I said. "So do I," Jack admitted. "All the time.

As you walk farther into the room it becomes a field of endless streetlamps, the stripes repeating in fractal patterns, over and over and over.

There is only one miracle but it is a fractal.

Why is geometry often described as ""cold" and ""dry?" One reason lies in its inability to describe the shape of a cloud, a mountain, a coastline, or a tree. Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.

The two dominant components that constitute a city, its physical infrastructure and its socioeconomic activity, can both be conceptualized as approximately self-similar fractal-like network structures.

Examples of fractals are everywhere in nature. They can be found in the patterns of trees, branches, and ferns, in which each part appears to be a smaller image of the whole. They are found in the branch-like patterns of river systems, lightning, and blood vessels. They can be seen in snowflakes, seashells, crystals, and mountain ranges. We can even see the holographic and fractal-like nature of reality in the structure of the Universe itself, as the clusters of galaxies and dark matter resemble the neurons in our brain, the mycelium network of fungi, as well as the network of the man-made Internet.

All high mathematics serves to do is to beget higher mathematics.

«Per­ho­nen is not here any­more,» it says, with a voice made of wings and whis­pers.

Across the world millions of lives are altered by the absence of the dead, but three members of Teddy's last crew—Clifford the bomb-aimer, Fraser, the injured pilot, and Charlie, the tail-end Charlie—all bail out successfully from F-Fox and see out the rest of the war in a POW camp. On their return they all marry and have children, fractals of the future.

Know that she was a good and hardworking intern, and that she died doing what she loved: simultaneously living and dying in infinite, fractal defiance of linear time.

It was sunset, and the flat, highway-veined city was just beginning to glimmer with electric light, civilization pulsing across the ground in arteries, in fractals.

Freewill is fractal.

Though blessed with the enviable properties of a mink coat—graceful, unreasonable, and impractical no matter what she was draped over—she was nevertheless one of those people whose personality proved to be the bane of modern mathematicians. She was neither a flat nor solid shape. She showed no symmetry at all. Trigonometry, Calculus and Statistics all proved useless. Her Pie Chart was a muddle of arbitrary wedges, her Line Graph, the silhouette of the Alps. And just when one listed her under Chaos Theory—Butterfly Effects, Weather Predictions, Fractals, Bifurcation diagrams and whatnot—she showed up as an equilateral triangle, sometimes even a square.

Human violence as a kind of fractal—self-similar on all scales from bar fight to system-wide war. The buildup of insults and lost face that swelled over the course of an evening or a century. The shoving and shoving back, neither side sure they wanted to escalate and uncertain how to back down.

gold light burned faintly. From his cosy window seat, Mario was tracing a frost-flower on the windowpane with an unsure finger. Were its perfectly-rendered geometric patterns a product of nature, or were they an artefact of metaphysics? Was the frost-flower to the Masters what a work of Art was to him? Did the Masters of Strings truly control every aspect of reality? The fractal flower slowly melted under Mario’s fingertip. “No work of chance here,” he bitterly thought. “This was by design.

One simple but powerful consequence of the fractal geometry of surfaces is that surfaces in contact do not touch everywhere. The bumpiness at all scales prevents that. Even in rock under enormous pressure, at some sufficiently small scale it becomes clear that gaps remain, allowing fluid to flow.

Because, you see, everything you know about the way this universe works is correct—except for the little problem that this isn’t the only universe we have to worry about. Information can leak between one universe and another. And in a vanishingly small number of the other universes there are things that listen, and talk back—see Al-Hazred, Nietzsche, Lovecraft, Poe, et cetera. The many-angled ones, as they say, live at the bottom of the Mandelbrot set, except when a suitable incantation in the platonic realm of mathematics—computerised or otherwise—draws them forth. (And you thought running that fractal screen-saver was good for your computer?)

A Fractal is a like a mathematical shape that is infinitely complex. In simple terms, it is a pattern that repeats forever. Every part of it, regardless of how it’s zoomed, in or out its parts look similar to the whole.

Cocoa-buttered girls were stretched out on the public beach in apparently random alignments, but maybe if a weather satellite zoomed in on one of those bodies and then zoomed back out, the photos would show the curving beach itself was another woman, a fractal image made up of the particulate sunbathers. All the beaches pressed together might form female landmasses, female continents, female planets and galaxies. No wonder men felt tense.

Jazz presumes that it would be nice if the four of us--simpatico dudes that we are--while playing this complicated song together, might somehow be free and autonomous as well. Tragically, this never quite works out. At best, we can only be free one or two at a time--while the other dudes hold onto the wire. Which is not to say that no one has tried to dispense with wires. Many have, and sometimes it works--but it doesn't feel like jazz when it does. The music simply drifts away into the stratosphere of formal dialectic, beyond our social concerns. Rock-and-roll, on the other hand, presumes that the four of us--as damaged and anti-social as we are--might possibly get it to-fucking-gether, man, and play this simple song. And play it right, okay? Just this once, in tune and on the beat. But we can't. The song's too simple, and we're too complicated and too excited. We try like hell, but the guitars distort, the intonation bends, and the beat just moves, imperceptibly, against our formal expectations, whetehr we want it to or not. Just because we're breathing, man. Thus, in the process of trying to play this very simple song together, we create this hurricane of noise, this infinitely complicated, fractal filigree of delicate distinctions. And you can thank the wanking eighties, if you wish, and digital sequencers, too, for proving to everyone that technologically "perfect" rock--like "free" jazz--sucks rockets. Because order sucks. I mean, look at the Stones. Keith Richards is always on top of the beat, and Bill Wyman, until he quit, was always behind it, because Richards is leading the band and Charlie Watts is listening to him and Wyman is listening to Watts. So the beat is sliding on those tiny neural lapses, not so you can tell, of course, but so you can feel it in your stomach. And the intonation is wavering, too, with the pulse in the finger on the amplified string. This is the delicacy of rock-and-roll, the bodily rhetoric of tiny increments, necessary imperfections, and contingent community. And it has its virtues, because jazz only works if we're trying to be free and are, in fact, together. Rock-and-roll works because we're all a bunch of flakes. That's something you can depend on, and a good thing too, because in the twentieth century, that's all there is: jazz and rock-and-roll. The rest is term papers and advertising.

The green fractals of the forest and the eons of faint star clusters above—my math’s teacher’s order in the universe—were nothing like the thoughts that jumped at me like thieves. When your friend has a boyfriend, you are supposed to back off.

The fractal structure nature has devised works so efficiently that, in most tissue, no cell is ever more than three or four cells away from a blood vessel. Yet the vessels and blood take up little space, no more than about five percent of the body.

Long live transfinite mountains, the hollow earth, time machines, fractal writing, aliens, dada, telepathy, flying saucers, warped space, teleportation, artificial reality, robots, pod people, hylozoism, endless shrinking, intelligent goo, antigravity, surrealism, software highs, two-dimensional time, gnarly computation, the art of photo composition, pleasure zappers, nanomachines, mind viruses, hyperspace, monsters from the deep and, of course, always and forever, the attack of the giant ants!

The thing about all complexes, splinter personalities, and fractal assignments is that they have no imagination. The can only replay the old events, scripts, and moribund outcome of their origin. But we do have an imagination, the power to image something new, or at least alternative.

No matter how much we have in common with someone, we will always have something that sets us apart; makes us different; unique. This is a good thing. Just think how boring the world would be if everyone were all the same!

The oldest fears were the most powerful. If there were gods, he thought for sure that the first and greatest—and evilest—would be the god of darkness. Light required effort. Light was a struggle. But the dark was easy, and it had existed before all else and would be there to envelop the universe in its smothering cloak when the last dim stars guttered out at the end of time.

Every unique thing in nature is related to the whole, and partakes of the perfection of the whole. Each particle is a microcosm, and faithfully renders the likeness of the world. In geometric harmony of the cosmos there are ways that resemble, there are universal patterns, from blood vessels, to winter trees or to a river delta, from nautilus shell to spiral galaxy, from neurons in the brain to the cosmic web. A whole universe of connections is in your mind – a universe within a universe – and one capable of reaching out to the other that gave rise to it. Billions of neurons touching billions of stars – surely spiritual.

In reality, a river's basic shape... is not a line but a tree. A river is, in its essence, a thing that branches... Although it flows inward toward its trunk, in geological time it grew, and continues to grow, outward, like an organism, from its ocean outlet to its many headwaters. In the vernacular of a new science, it is fractal, its structure echoing itself on all scales, from river to stream to brook to creek to rivulet, branches too small to name and too many to count.

A day is like a whole life. You start out doing one thing, but end up doing something else, plan to run an errand, but never get there.… And at the end of your life, your whole existence has that same haphazard quality, too. Your whole life has the same shape as a single day.” “I guess it’s one way to look at things,” Grant said. “No,” Malcolm said. “It’s the only way to look at things. At least, the only way that is true to reality. You see, the fractal idea of sameness carries within it an aspect of recursion, a kind of doubling back on itself, which means that events are unpredictable. That they can change suddenly, and without warning.

Were he now still among the living, Dr. Incandenza would now describe tennis in the paradoxical terms of what’s now called ‘Extra-Linear Dynamics.’ And Schtitt, whose knowledge of formal math is probably about equivalent to that of a Taiwanese kindergartner, nevertheless seemed to know what Hopman and van der Meer and Bollettieri seemed not to know: that locating beauty and art and magic and improvement and keys to excellence and victory in the prolix flux of match play is not a fractal matter of reducing chaos to a pattern. Seemed intuitively to sense that it was a matter not of reduction at all, but — perversely — of expansion, the aleatory flutter of uncontrolled, metastatic growth — each well-shot ball admitting of n possible responses, n² responses to those responses, and on into what Incandenza would articulate to anyone who shared both his backgrounds as a Cantorian continuum of infinities of possible move and response, Cantorian and beautiful because infoliating, contained, this diagnate infinity of infinities of choice and execution, mathematically uncontrolled but humanly contained, bounded by the talent and imagination of self and opponent, bent in on itself by the containing boundaries of skill and imagination that brought one player finally down, that kept both from winning, that made it, finally, a game, these boundaries of self.

Fractals are a kind of geometry, associated with a man named Mandelbrot. Unlike ordinary Euclidean geometry that everybody learns in school—squares and cubes and spheres—fractal geometry appears to describe real objects in the natural world. Mountains and clouds are fractal shapes. So fractals are probably related to reality. Somehow. “Well, Mandelbrot found a remarkable thing with his geometric tools. He found that things looked almost identical at different scales.” “At different scales?” Grant said. “For example,” Malcolm said, “a big mountain, seen from far away, has a certain rugged mountain shape. If you get closer, and examine a small peak of the big mountain, it will have the same mountain shape. In fact, you can go all the way down the scale to a tiny speck of rock, seen under a microscope—it will have the same basic fractal shape as the big mountain.

Jinni and lost jannahs are less to him than dust.

Sometimes the universe decided to rip apart your life and stomp on the pieces, and there wasn’t a damn thing you could do about it except say, “Now what?

Her entire being was like a wonderful yet horrible dream he wasn’t sure he could or would want to wake up from.

If reality is not what you want it to be, change it. You should not accept anything blindly, not death, not immortality.

There is no point in being upset if you are not prepared to do something about it.

God loves fractals!)

Just as it was not necessary for Beethoven to know the science of the physical manufacture of the instruments in his orchestra in order for him to compose, it is not necessary for you to understand vortex based mathematics, fractal field theory, dodecahedrons, geometric solids, calculus, Fibonacci series, centripetal force, and quantum physics in order to become enlightened.

While we think of the boundary between what is legal and what is not as a clear dividing line, it is far from being so. Rather, the boundary becomes further and further indented and folded over time, yielding a jagged and complicated border, rather than a clear straight line. In the end, the law turns out to look like a fractal: no matter how much you zoom in on such a shape, there is always more unevenness, more detail to observe. Any general rule must end up dealing with exceptions, which in turn split into further exceptions and rules, yielding an increasingly complicated, branching structure.

Even when I’m caught off guard by a lathery shade of peach on the bottom corner of a painting at the Met, as if being reminded that I haven’t seen all the colors, and how there’s more to see, and how one color’s newness can invalidate all of my sureness. To experience infinity and sometimes too the teasing melancholy born from the smallest breakthroughs, like an unanticipated shade of peach, like Buster Keaton smiling, or my friend Doreen’s laugh—how living and opposite of halfhearted it is. Or my beautiful mother growing out her gray, or a lightning bolt’s fractal scarring on a human body, or Fantin-Latour’s hollyhocks, or the sound of someone practicing an instrument—the most sonically earnest sound. Or how staring at ocean water so blue, it leaves me bereft. In postcards, I’ll scribble “So blue!” because, what else?

That it’s what makes room for the universes inside you, all the endless inbent fractals of connection and symphonies of different voices, the infinities you can never show another soul. And you think it makes you a fraud, the tiny fraction anyone else ever sees? Of course you’re a fraud, of course what people see is never you. And of course you know it’s only a part. Who wouldn’t? It’s called free will, Sherlock. But at the same time it’s why it feels so good to break down and cry in front of others, or to laugh, or speak in tongues, or chant in Bengali- it’s not English anymore, it’s not getting squeezed through any hole.

The truth is you already know what it’s like. You already know the difference between the size and speed of everything that flashes through you and the tiny inadequate bit of it all you can ever let anyone know. As though inside you is this enormous room full of what seems like everything in the whole universe at one time or another and yet the only parts that get out have to somehow squeeze out through one of those tiny keyholes you see under the knob in older doors. As if we are all trying to see each other through these tiny keyholes. But it does have a knob, the door can open. But not in the way you think. But what if you could? Think for a second — what if all the infinitely dense and shifting worlds of stuff inside you every moment of your life turned out now to be somehow fully open and expressible afterward, after what you think of as you has died, because what if afterward now each moment itself is an infinite sea or span or passage of time in which to express it or convey it, and you don’t even need any organized English, you can as they say open the door and be in anyone else’s room in all your own multiform forms and ideas and facets? Because listen — we don’t have much time, here’s where Lily Cache slopes slightly down and the banks start getting steep, and you can just make out the outlines of the unlit sign for the farmstand that’s never open anymore, the last sign before the bridge — so listen: What exactly do you think you are? The millions and trillions of thoughts, memories, juxtapositions — even crazy ones like this, you’re thinking — that flash through your head and disappear? Some sum or remainder of these? Your history? Do you know how long it’s been since I told you I was a fraud? Do you remember you were looking at the respicem watch hanging from the rearview and seeing the time, 9:17? What are you looking at right now? Coincidence? What if no time has passed at all?* The truth is you’ve already heard this. That this is what it’s like. That it’s what makes room for the universes inside you, all the endless inbent fractals of connection and symphonies of different voices, the infinities you can never show another soul. And you think it makes you a fraud, the tiny fraction anyone else ever sees? Of course you’re a fraud, of course what people see is never you. And of course you know this, and of course you try to manage what part they see if you know it’s only a part. Who wouldn’t? It’s called free will, Sherlock. But at the same time it’s why it feels so good to break down and cry in front of others, or to laugh, or speak in tongues, or chant in Bengali — it’s not English anymore, it’s not getting squeezed through any hole. So cry all you want, I won’t tell anybody.

He’d learned early to carve and mold and cover the parts of himself that didn’t fit into the world. Keep the fractals of himself hidden, the way he came up at harsh angles to everyone else. He was a kaleidoscope, shifting and changing in the light. What was true was kept in the shadows, the same shadows that lived in his bones, that covered the memories of praying beside his father in the sunlight, murmuring the Quran.

At the fourth, the fractal (or viral, or radiant) stage of value, there is no point of reference at all, and value radiates in all directions, occupying all interstices, without reference to anything whatsoever, by virtue of pure contiguity. At the fractal stage there is no longer any equivalence, whether natural or general. Properly speaking there is now no law of value, merely a sort of epidemic of value, a sort of general metastasis of value, a haphazard proliferation and dispersal of value. Indeed, we should really no longer speak of 'value' at all, for this kind of propagation or chain reaction makes all valuation possible.

As he ran through the dense understory, he could read the signs of arboreal intrigue, the drama and power struggles as species vied for control over a patch of sunlight, or giant firs and fungal spores opted to work together for their mutual benefit. He could see time unfolding here, and history, embedded in the whorls and fractal forms of nature, and he would come home, sweating and breathless, and tell her what he’d seen.

Like a fractal, wetiko operates on multiple dimensions simultaneously--intra-personally (within individuals), inter-personally (among ourselves), collectively (as a species), as well as trans-personally (in a realm beyond our personal selves). Those afflicted with wetiko consume, like a cannibal, the life force of others--human and nonhuman--for private purposes or profit, and do so without giving back something from their own lives.

In short, what Brown, Enquist, and West are saying is that evolution structured our circulatory systems as fractal networks to approximate a “fourth dimension” so as to make our metabolisms more efficient. As West, Brown, and Enquist put it, “Although living things occupy a three-dimensional space, their internal physiology and anatomy operate as if they were four-dimensional … Fractal geometry has literally given life an added dimension.

Even more important is the way complex systems seem to strike a balance between the need for order and the imperative for change. Complex systems tend to locate themselves at a place we call “the edge of chaos.” We imagine the edge of chaos as a place where there is enough innovation to keep a living system vibrant, and enough stability to keep it from collapsing into anarchy. It is a zone of conflict and upheaval, where the old and new are constantly at war. Finding the balance point must be a delicate matter—if a living system drifts too close, it risks falling over into incoherence and dissolution; but if the system moves too far away from the edge, it becomes rigid, frozen, totalitarian. Both conditions lead to extinction. . . . Only at the edge of chaos can complex systems flourish.8 This threshold line, that edge between anarchy and frozen rigidity, is not a like a fence line, it is a fractal line; it possesses nonlinearity.

On Westminster Bridge, Arthur was struck by the brightness of the streetlamps running across like a formation of stars. They shone white against the black coats of the marching gentlefold and fuller than the moon against the fractal spires of Westminster. They were, Arthur quickly realized, the new electric lights, which the city government was installing, avenue by avenue, square by square, in place of the dirty gas lamps that had lit London's public spaces for a century. These new electric ones were brighter. They were cheaper. They required less maintenance. And they shone farther into the dime evening, exposing every crack in the pavement, every plump turtle sheel of stone underfoot. So long to the faint chiaroscuro of London, to the ladies and gentlemen in black-on-black relief. So long to the era of mist and carbonized Newcastle coal, to the stench of the Blackfriars foundry. Welcome to the cleasing glare of the twentieth century.

I find that most people serve practical needs. They have an understanding of the difference between meaning and relevance. And at some level my mind is more interested in meaning than in relevance. That is similar to the mind of an artist. The arts are not life. They are not serving life. The arts are the cuckoo child of life. Because the meaning of life is to eat. You know, life is evolution and evolution is about eating. It's pretty gross if you think about it. Evolution is about getting eaten by monsters. Don't go into the desert and perish there, because it's going to be a waste. If you're lucky the monsters that eat you are your own children. And eventually the search for evolution will, if evolution reaches its global optimum, it will be the perfect devourer. The thing that is able to digest anything and turn it into structure to sustain and perpetuate itself, for long as the local puddle of negentropy is available. And in a way we are yeast. Everything we do, all the complexity that we create, all the structures we build, is to erect some surfaces on which to out compete other kinds of yeast. And if you realize this you can try to get behind this and I think the solution to this is fascism. Fascism is a mode of organization of society in which the individual is a cell in the superorganism and the value of the individual is exactly the contribution to the superorganism. And when the contribution is negative then the superorganism kills it in order to be fitter in the competition against other superorganisms. And it's totally brutal. I don't like fascism because it's going to kill a lot of minds I like. And the arts is slightly different. It's a mutation that is arguably not completely adaptive. It's one where people fall in love with the loss function. Where you think that your mental representation is the intrinsically important thing. That you try to capture a conscious state for its own sake, because you think that matters. The true artist in my view is somebody who captures conscious states and that's the only reason why they eat. So you eat to make art. And another person makes art to eat. And these are of course the ends of a spectrum and the truth is often somewhere in the middle, but in a way there is this fundamental distinction. And there are in some sense the true scientists which are trying to figure out something about the universe. They are trying to reflect it. And it's an artistic process in a way. It's an attempt to be a reflection to this universe. You see there is this amazing vast darkness which is the universe. There's all these iterations of patterns, but mostly there is nothing interesting happening in these patterns. It's a giant fractal and most of it is just boring. And at a brief moment in the evolution of the universe there are planetary surfaces and negentropy gradients that allow for the creation of structure and then there are some brief flashes of consciousness in all this vast darkness. And these brief flashes of consciousness can reflect the universe and maybe even figure out what it is. It's the only chance that we have. Right? This is amazing. Why not do this? Life is short. This is the thing we can do.

When energy is poured into a system, and the system dissipates that energy in its slide toward entropy, it can become poised in an orderly, indeed beautiful, configuration—a sphere, spiral, starburst, whirlpool, ripple, crystal, or fractal. The fact that we find these configurations beautiful, incidentally, suggests that beauty may not just be in the eye of the beholder. The brain’s aesthetic response may be a receptiveness to the counter-entropic patterns that can spring forth from nature.

ideas are the lifeblood of civilisation, and societies assimilate ideas and become comfortable with their implications through understanding and debate. If eternal inflation is the correct description of our universe, it will be the artists, philosophers, theologians, novelists and musicians, alongside the physicists, who explore its meaning. What does it mean if the existence of our universe is inevitable? What does it mean if we are not special in any way? What does it mean if our observable universe, with all its myriad galaxies and possibilities, is a vanishingly small leaf on an every-expanding fractal tree of universes? What does it mean if you are, because you have to be? I can’t tell you. I can only ask – what does it mean to you?

The truth is you've already heard this. That this is what it's like. That it's what makes room for the universes inside you, all the endless inbent fractals of connection and symphonies of different voices, the infinities you can never show another soul. And you think it makes you a fraud, the tiny fraction anyone else ever sees? Of course you're a fraud, of course what people see is never you. And of course you know this, and of course you try to manage what part they see if you know it's only a part. Who wouldn't? It's called free will, Sherlock. But at the same time it's why it feels so good to break down and cry in front of others, or to laugh, or speak in tongues, or chant in Bengali--it's not English anymore, it's not getting squeezed through any hole.

The Great Pyramid was a fractal resonator for the entire Earth. It is designed according to the proportions of the cosmic temple, the natural pattern that blends the two fundamental principles of creation. The pyramid has golden ratio, pi, the base of natural logarithms, the precise length of the year and the dimensions of the Earth built into its geometry. It demonstrates.... As John Michell has pointed out in his wonderful little book, City of Revelation, 'Above all, the Great Pyramid is a monument to the art of 'squaring the circle''.

Examined in color through the adjustable window of a computer screen, the Mandelbrot set seems more fractal than fractals, so rich is its complication across scales. A cataloguing of the different images within it or a numerical description of the set's outline would require an infinity of information. But here is a paradox: to send a full description of the set over a transmission line requires just a few dozen characters of code. A terse computer program contains enough information to reproduce the entire set. Those who were first to understand the way the set commingles complexity and simplicity were caught unprepared—even Mandelbrot.

Everything is fields, and a particle is just a smaller version of a field. There is a harmonic relationship involved. Disturbing ideas like those of Einstein in 1905 and Feynman Pocono Conference in 1948. Here we go; 1) The universe is ringing like a bell. Neil Turok's Public Lecture: The Astonishing Simplicity of Everything. 2) The stuff of the universe is waves or fields. 3) Scale is relative, not fixed because all of these waves are ratios of one another. 4) The geometry is fractal. This could be physical or computational. 5) If the geometry is computational then, there is no point in speaking about the relationship of the pixels on the display.

No one is alone in this world. No act is without consequences for others. It is a tenet of chaos theory that, in dynamical systems, the outcome of any process is sensitive to its starting point-or, in the famous cliche, the flap of a butterfly's wings in the Amazon can cause a tornado in Texas. I do not assert markets are chaotic, though my fractal geometry is one of the primary mathematical tools of "chaology." But clearly, the global economy is an unfathomably complicated machine. To all the complexity of the physical world of weather, crops, ores, and factories, you add the psychological complexity of men acting on their fleeting expectations of what may or may not happen-sheer phantasms. Companies and stock prices, trade flows and currency rates, crop yields and commodity futures-all are inter-related to one degree or another, in ways we have barely begun to understand. In such a world, it is common sense that events in the distant past continue to echo in the present.

The Universe that the quantum gods made is cruel and random.

. . .biographers tend to regard as character those elements of personality that remain constant, or nearly so, throughout. . .Like practitioners of fractal geometry, biographers seek patterns that persist as one moves from micro- to macro-levels of analysis, and back again. . . . It follows from this that the scale across which we seek similarity need not be chronological. Consider the following incidents in the life of Stalin between 1929 and 1940, arranged not by dates but in terms of ascending horror. Start with the parrot he kept in a cage in his Kremlin apartment. The dictator had the habit of pacing up and down for long periods of time, smoking his pipe, brooding, and occasionally spitting on the floor. One day the parrot tried to mimic Stalin's spitting. He immediately reached into the cage with his pipe and crushed the parrot's head. A very micro-level event, you might well say, so what? But then you learn that Stalin, while on vacation in the Crimea, was once kept awake by a barking dog. It turned out to be a seeing-eye dog that belonged to a blind peasant. The dog wound up being shot, and the peasant wound up in the Gulag. And then you learn that Stalin drove his independently minded second wife, who tried to talk back to him, into committing suicide. And that he arranged for Trotsky, who also talked back, to be assassinated halfway around the world. And that he arranged as well the deaths of as many of Trotsky's associates that he could reach, as well as the deaths of hundred of thousands of other people who never had anything to do with Trotsky. And that when his own people began to talk back by resisting the collectivization of agriculture, he allowed some fourteen million of them to die from the resulting starvation, exile, or imprisonment. Again, there's self-similarity across scale, except that the scale this time is a body count. It's a fractal geometry of terror. Stalin's character extended across time and space, to be sure, but what's most striking about it is its extension across scale: the fact that his behavior seemed much the same in large matters, small matters, and most of those that lay in between.

locating beauty and art and magic and improvement and keys to excellence and victory in the prolix flux of match play is not a fractal matter of reducing chaos to pattern. Seemed intuitively to sense that it was a matter not of reduction at all, but—perversely—of expansion, the aleatory flutter of uncontrolled, metastatic growth—each well-shot ball admitting of n possible responses, n2 possible responses to those responses, and on into what Incandenza would articulate to anyone who shared both his backgrounds as a Cantorian 35 continuum of infinities of possible move and response, Cantorian and beautiful because infoliating, contained, this diagnate infinity of infinities of choice and execution, mathematically uncontrolled but humanly contained, bounded by the talent and imagination of self and opponent, bent in on itself by the containing boundaries of skill and imagination that brought one player finally down, that kept both from winning, that made it, finally, a game, these boundaries of self. ‘You

Olo, Remi, Kwuga, Nur, Anajama, Rhoden. Only Olo and Remi were in my group. Everyone else I met in the dining area or the learning room where various lectures were held by professors onboard the ship. They were all girls who grew up in sprawling houses, who’d never walked through the desert, who’d never stepped on a snake in the dry grass. They were girls who could not stand the rays of Earth’s sun unless it was shining through a tinted window. Yet they were girls who knew what I meant when I spoke of “treeing.” We sat in my room (because, having so few travel items, mine was the emptiest) and challenged each other to look out at the stars and imagine the most complex equation and then split it in half and then in half again and again. When you do math fractals long enough, you kick yourself into treeing just enough to get lost in the shallows of the mathematical sea. None of us would have made it into the university if we couldn’t tree, but it’s not easy. We were the best and we pushed each other to get closer to “God.

Engineers had not framework for understanding Mandelbrot's description, but mathematicians did. In effect, Mandelbrot was duplicating an abstract construction known as the Cantor set, after the nineteenth-century mathematician Georg Cantor. To make a Cantor set, you start with the interval of numbers from zero to one, represented by a line segment. Then you remove the middle third. That leaves two segments, and you remove the middle third of each (from one-ninth to two-ninths and from seven-ninths to eight-ninths). That leaves four segments, and you remove the middle third of each- and so on to infinity. What remains? A strange "dust" of points, arranged in clusters, infinitely many yet infinitely sparse. Mandelbrot was thinking of transmission errors as a Cantor set arranged in time.

But it wasn't just the bird, was it, Teddy thought as he lay in bed waiting for sleep to find him, the nightly oblivion kept at bay by meandering thought. It wasn't just the one lark that had been silenced by Izzie. (A mouthful.) It was the generations of birds that would have come after it and now would never be born. All those beautiful songs that would never be sung. Later in his life he learned the word "exponential," and later still the world "fractal," but for now it was a flock that grew larger and larger as it disappeared into a future that would never be.

In the heaven of the great god Indra is said to be a vast and shimmering net, finer than a spider’s web, stretching to the outermost reaches of space. Strung at the each intersection of its diaphanous threads is a reflecting pearl. Since the net is infinite in extent, the pearls are infinite in number. In the glistening surface of each pearl are reflected all the other pearls, even those in the furthest corners of the heavens. In each reflection, again are reflected all the infinitely many other pearls, so that by this process, reflections of reflections continue without end.

If we increase r [in a logistic map] even more, we will eventually force the system into a period-8 limit cycle, then a period-16 cycle, and so on. The amount that we have to increase r to get another period doubling gets smaller and smaller for each new bifurcation. This cascade of period doublings is reminiscent of the race between Achilles and the tortoise, in that an infinite number of bifurcations (or time steps in the race) can be confined to a local region of finite size. At a very special critical value, the dynamical system will fall into what is essentially an infinite-period limit cycle. This is chaos.

Where is the freedom in all this? Nowhere! There is no choice here, no final decision. All decisions concerning networks, screens, information or communication are serial in character, partial, fragmentary, fractal. A mere succession of partial decisions, a microscopic series of partial sequences and objectives, constitute as much the photographer's way of proceeding as that of Telecomputer Man in general, or even that called for by our own most trivial television viewing. All such behaviour is structured in quantum fashion, composed of haphazard sequences of discrete decisions. The fascination derives from the pull of the black box, the appeal of an uncertainty which puts paid to our freedom. Am I a man or a machine? This anthropological question no longer has an answer. We are thus in some sense witness to the end of anthropology, now being conjured away by the most recent machines and technologies. The uncertainty here is born of the perfecting of machine networks, just as sexual uncertainty (Am I a man or a woman? What has the difference between the sexes become?) is born of increasingly sophisticated manipulation of the unconscious and of the body, and just as science's uncertainty about the status of its object is born of the sophistication of analysis in the microsciences.

From predator-prey models (the so-called Lotka-Volterra type of population dynamics), I knew that populations will experience Extremistan-style variability, hence predators will necessarily go through periods of feast and famine. That's us, humans-we had to have been designed to experience extreme hunger and extreme abundance. So our food intake had to have been fractal. Not a single one of those promoting the "three meals a day," "eat in moderation" idea has tested it empirically to see whether it is healthier than intermittent fasts followed by large feasts. But Near Eastern religions (Judaism, Islam, and Orthodox Christianity) knew it, of course-just as they knew the need for debt avoidance-and so they had fast days.

that’s how things are. A day is like a whole life. You start out doing one thing, but end up doing something else, plan to run an errand, but never get there.… And at the end of your life, your whole existence has that same haphazard quality, too. Your whole life has the same shape as a single day.” “I guess it’s one way to look at things,” Grant said. “No,” Malcolm said. “It’s the only way to look at things. At least, the only way that is true to reality. You see, the fractal idea of sameness carries within it an aspect of recursion, a kind of doubling back on itself, which means that events are unpredictable. That they can change suddenly, and without warning.” “Okay …” “But we have soothed ourselves into imagining sudden change as something that happens outside the normal order of things. An accident, like a car crash. Or beyond our control, like a fatal illness. We do not conceive of sudden, radical, irrational change as built into the very fabric of existence. Yet it is. And chaos theory teaches us,” Malcolm said, “that straight linearity, which we have come to take for granted in everything from physics to fiction, simply does not exist. Linearity is an artificial way of viewing the world. Real life isn’t a series of interconnected events occurring one after another like beads strung on a necklace. Life is actually a series of encounters in which one event may change those that follow in a wholly unpredictable, even devastating way.” Malcolm sat back in his seat, looking toward the other Land Cruiser, a few yards ahead. “That’s a deep truth about the structure of our universe. But, for some reason, we insist on behaving as if it were not true.

Meanwhile, people are busy using fractals to explain any system that has defied other, more reductionist approaches. Since they were successfully applied by IBM's Benoit Mandlebrot to the problem of seemingly random, intermittent interference on the phone lines, fractals have been used to identify underlying patterns in weather systems, computer files, and bacteria cultures. Sometimes fractal enthusiasts go a bit too far, however, using these nonlinear equations to mine for patterns in systems where none exist. Applied to the stock market to consumer behavior, fractals may tell less about those systems than about the people searching for patterns within them. There is a dual nature to fractals: They orient us while at the same time challenging our sense of scale and appropriateness. They offer us access to the underlying patterns of complex systems while at the same time tempting us to look for patterns where none exist. This makes them a terrific icon for the sort of pattern recognition associated with present shock—a syndrome we'll call factalnoia. Like the robots on Mystery Science Theater 3000, we engage by relating one thing to another, even when the relationship is forced or imagined. The tsunami makes sense once it is connected to chemtrails, which make sense when they are connected to HAARP. It's not just conspiracy theorists drawing fractalnoid connections between things. In a world without time, any and all sense making must occur on the fly. Simultaneity often seems like all we have. That's why anyone contending with present shock will have a propensity to make connections between things happening in the same moment—as if there had to be an underlying logic.