Fractal Quotes

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. ~ Nassim Nicholas Taleb

The universe is fractal. The closer you look at it, the more interesting it becomes. ~ John Lloyd

I make fractals. They're like mathematical pictures. My stepdad is actually a rocket scientist, so in his free time, he gave me a fractal program for fun. He showed me how to use it when I was about nine or 10, and I made thousands of fractals. ~ Ronda Rousey

Any issue and any problem, no matter what height you look at it from, no matter how much you extend past the first fractal, it's still a fractal of something that emanates from within your consciousness - from within the human consciousness. And it'll move on and manifest itself externally, and then those are what we pick up as societal ills. But all these battles we're fighting are internal. For me, it's reconciling hope with dread and trying to cut out some place in my mind where my heart can be protected a little bit. ~ El-P

Ideology is a straight-edge ruler in a fractal universe. ~ Marilynne Robinson

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. ~ David Bayles

If you have a hammer, use it everywhere you can, but I do not claim that everything is fractal. ~ Benoit Mandelbrot

In short, the idea dawns that the one universal principle which possibly ... between force and structure, the embodiment of the Principle of Least Action and the (unknown) force, which in mathematics is known as the attractor which pulls ... in the direction of the most optimal and relatively stable self-organized criticality, could very well be the Golden Ratio dynamic. the universal principle which as the balance between finiteness and infinity, stability and flexibility underlies self-similar fractal forms emerging at the 'edge of chaos' indeed seems to be the Golden Ratio Spiral. ~ Marja De Vries

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. ~ Terry Pratchett

The simple equations that generate the convoluted Mandelbrot fractal have been called the wittiest remarks ever made. ~ John Allen Paulos

The first of the request prayers in the daily Amidah is a fractal. It replicates in miniature the structure of the Amidah as a whole. ~ Jonathan Sacks

A fighter, muses Rachel, is a fighter through and through, consistently irregular, a fighting man on every scale. Fractal, fractious, with a rough complexity! Nothing she can do. A fractal, Papa once told her, is a way of seeing infinity.

In Zachariah, she sees infinity.

Mandelbrot famously wrote a paper called 'How Long Is the Coast of Britain?,' the answer to which, of course, is that it depends how you look at it. The closer one looks, the larger it is. And more and more intricate, on an infinite scale.

There is a template for all things. ~ Emma Richler

. . .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, ~ John Lewis Gaddis

The theory of chaos and theory of fractals are separate, but have very strong intersections. That is one part of chaos theory is geometrically expressed by fractal shapes. ~ Benoit Mandelbrot

Astronomers had already found the fingerprints of chaos in violence on the sun's surface, gaps in the asteroid belt, and the distribution of galaxies. Levin and her colleagues have found them in the exit from the big bang and in black holes. They predict that light trapped by a black hole can enter unstable chaotic orbits and be reemited-making the black hole visible, if only briefly. Yes, chaos can light up black holes. "There are rational numbers to mine, fractal sets, and all kinds of truly beautiful consequences," she says. "So on the one hand, people are horrified, on the other they're mesmerized." She does chaos in curved space-time. Einstein would be proud. ~ James Gleick

I probably spend more time writing than reading science fiction. I find that science-fiction literature is so reactive to all the literature that's gone before that it's sort of like a fractal. It's gone to a level of detail that the average person could not possibly follow unless you're a fan. It iterates upon many prior generations of iterations. ~ James Cameron

The decline of violence is a fractal phenomenon. You can see it over millennia, over centuries, over decades and over years. ~ Steven Pinker

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. ~ Erin Morgenstern

I started collecting aerial photographs of Native American and South Pacific architecture; only the African ones were fractal. And if you think about it, all these different societies have different geometric design themes that they use. So Native Americans use a combination of circular symmetry and fourfold symmetry. ~ Ron Eglash

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. ~ Jean Baudrillard

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. ~ James S.A. Corey

If dimensions are virtual like the particles in quantum foam are virtual then, entanglement is information that is in more than one location (hologram).
There are no particles, they may be wave packets but the idea of quantum is, a precise ratio of action in relationship to the environment.
Feynman's path integral is not infinite, it is fractal.
If you look at a star many light years away, the photon that hits your eye leaves the star precisely when the timing for the journey will end at your eye because the virtual dimension of the journey is zero distance or zero time. Wheeler said that if your eye is not there to receive the photon then it won't leave the star in the distant past. If the dimension in the direction of travel is zero, you have a different relationship then if it is zero time in terms of the property of the virtual dimensions.

Is a particle really a wave packet?
Could something like a "phase transition" involve dimensions that are more transitory then we imagined.
Example; a photon as a two dimensional sheet is absorbed by an electron so that the photon becomes a part of the geometry of the electron in which the electrons dimensions change in some manner.
Could "scale" have more variation and influence on space and time that our models currently predict?
Could information, scale, and gravity be intimately related? ~ R.A. Delmonico

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. ~ Isaac Asimov

IN THE MIND'S EYE, a fractal is a way of seeing infinity. ~ James Gleick

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. ~ Peter Watts

All created forms are fractal, as is their purpose, use, and allotted time for existence. ~ Guy Finley

My assumption was that all indigenous architecture would be more fractal. My reasoning was that all indigenous architecture tends to be organized from the bottom up. As it turns out, though, my reasoning was wrong. ~ Ron Eglash

At very best there are two problems with ideology. The first is that it does not represent or conform to or even address reality. It is a straight-edge ruler of a fractal universe. And the second is that it inspires in its believers the notion that the fault here lies with miscreant fact, which should therefore be conformed to the requirements of theory by all means necessary. To the ideologue this would amount to putting the world right, ridding it of ambiguity and of those tedious and endless moral and ethical questions that dog us through life, and that those around us so rarely answer to our satisfaction. ~ Marilynne Robinson

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. ~ Samuel Arbesman

Thus wuwei manifests itself in the adaptive integration of the interacting parts of units of a complex system. The tendency of wuwei is to lead a system toward a state of fractal congruence, a close fitting together, a coalescing, of its significant components. The cooperation of those components facilitates the functioning of the system on its new holistic level. At the highest levels of complexity, wuwei integrates human beings into the systems of the world. This process of integration represents a synergistic enhancement of Dao by empathic human participants in cooperation with nature and with the outgrowths of human nature that have emerged from our evolutionary history and constitute culture. Thus, a fractal self is such a human being who is a participant with others, open to various worlds within nature and culture, and this person becomes a potential facilitator of emergence. ~ David Jones

Fractal geometry is everywhere, even in lines drawn in the sand. It's the cycle of life ... You see fractals in plants, in flowers. Within the human lung are branches within branches. ~ Ron Eglash

There is only one miracle but it is a fractal. ~ R.A.Delmonico

At the earliest drawings of the fractal curve, few clues to the underlying mathematical structure will be seen. ~ Louis L'Amour

It was a fractal of ugliness, disgusting at every level of self-similarity. ~ Eliezer Yudkowsky

Both chaos theory and fractal have had contacts in the past when they are both impossible to develop and in a certain sense not ready to be developed. ~ Benoit Mandelbrot

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. ~ Steve Aylett

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. ~ Adrienne Maree Brown

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

At the very best there are two major problems with ideology. The first is that it does not represent or conform to or even address reality. It is a straight-edge ruler in a fractal universe. And the second is that it inspires in its believers the notion that the fault here lies with miscreant fact, which should therefore be conformed to the requirements of theory by all means necessary. ~ Marilynne Robinson

Nowhere else in history has there ever been a flag that stands for the right to burn itself. This is the fractal of our flag. It stands for the right to destroy itself. ~ Ken Kesey

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. ~ Graham Moore

I've been thinking about what you told me Friday night, about having a broken brain, not a broken spirit. And I've been thinking about what it means to be broken, and how we call things broken that aren't - fractured. It made me think about fractals. Do you know what a Mandelbrot Set is? [...] So, a Mandelbrot Set is one kind of fractal. All fractals are self similar, which means they have a pattern that repeats at different levels of magnification. Fractals are infinitely recursive and orderly, but they appear to be chaotic. [...] Mathematicians use fractals to model things that appear to be chaotic but are really accumulations of complex patterns. Fractured things - not broken, because broken implies that there is a normal, when mathematically there isn't. Normal would simply mean easily predictable, like a salt crystal. Fractured things like snowflakes and mountain ranges are more geometrically interesting and require more complex modeling. [...] You are a fractured snowflake, a pattern, repeated in infinite detail in a world full of salt crystals. You're not broken, you're perfect. ~ Laura Creedle

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?) ~ Charles Stross

I conceived, developed and applied in many areas a new geometry of nature, which finds order in chaotic shapes and processes. It grew without a name until 1975, when I coined a new word to denote it, fractal geometry, from the Latin word for irregular and broken up, fractus. Today you might say that, until fractal geometry became organized, my life had followed a fractal orbit. ~ Benoit Mandelbrot

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. ~ Wm. Paul Young

Fractal Beats The body structures of all of nature's animals are fractal, and so too is their behaviour (see Orchid Fractals) and even their timing. Our heart beats seem regular and rhythmic, but when the structure of the timing is examined in fine detail, it is revealed to be very slightly fractal. And this is very important. ~ Nigel Lesmoir-Gordon

Her mind wandered a little bit during the slow moments. 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. All of that was the history of the inner planets and the Belt since the beginning. Then Marco had thrown his sucker punch and sent the system reeling back. Since then, feints and evaluations, flurries of violence that weren't meant to end anything so much as find position, test the opponent. Everything ~ James S.A. Corey

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. ~ James Gleick

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. ~ David Levithan

You're a refraction of the one light. You're a waveform of light. You're a fractal, a pattern that continuously changes. ~ Frederick Lenz

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! ~ Rudy Rucker

The physics of earthquake behavior is mostly independent of scale. A large earthquake is just a scaled-up version of a small earthquake. That distinguishes earthquakes from animals, for example-a ten inch animal must be structured quite differently from a one-inch animal, and a hundred-inch animal needs a different architecture still, if its bones are not to snap under the increased mass. Clouds, on the other hand, are scaling phenomena like earthquakes. Their characteristic irregularity-describable in terms of fractal dimension-changes not at all as they are observed on different scales. That is why air travelers lose all perspective on how far away a cloud is. Without help from cues such as haziness, a cloud twenty feet away can be indistinguishable from two thousand feet away. Indeed, analysis of satellite pictures has shown an invariant fractal dimension in clouds observed from hundreds of miles away. ~ James Gleick

There's a theory that says that life is based on a competition and the struggle and the fight for survival, and it's interesting because when you look at the fractal character of evolution, it's totally different. It's based on cooperation among the elements in the geometry and not competition. ~ Bruce Lipton

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

I spent half my life, roughly speaking, doing the study of nature in many aspects and half of my life studying completely artificial shapes. And the two are extraordinarily close; in one way both are fractal. ~ Benoit Mandelbrot

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. ~ James Gleick

I fell in love with flora of all types, especially ferns. Loved the sparse structure and repetition of shape - almost fractal. ~ Jack Dorsey

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 Stone ~ Dave Hickey

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. ~ David Levithan