Fractal Quotes & Sayings

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. — Kate Atkinson

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

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

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

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

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

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

Enchanting is not the word that would immediately spring to mind when describing a play that deals with fractal geometry, iterated algorithms, chaos theory and the second law of thermodynamics, but it is a perfect fit for Tom Stoppard's astonishing 1993 play, which is as beautiful as it is brilliant. This is one Stoppard drama that you don't have to be Einstein to understand
you can feel it as well as think it. ( ... ) Breathtaking, exhilarating and deeply satisfying. — Lyn Gardner

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

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

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

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

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

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

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

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. — Bonnie Jo Campbell

Redwoods have an enormous surface area that extends upward into space because they have a propensity to do something called reiteration. A redwood is a fractal. And as they put out limbs, the limbs burst into small trees, copies of the redwood. — Richard Preston

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

While fractal geometry is often used in high-tech science, its patterns are surprisingly common in traditional African designs. — Ron Eglash

Fractal geometry is not just a chapter of mathematics, but one that helps Everyman to see the same world differently. — Benoit Mandelbrot

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

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. — James Gleick

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'. — Alison Charlotte Primrose

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

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

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. — Joseph Fink

Creating a body of mathematics is about intellectual labor, not some kind of transcendental revelation. There are plenty of important components of European fractal geometry that are missing from the African version. — Ron Eglash

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

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

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

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

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

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

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

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

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

Mathematicians didn't invent infinity until 1877. So they thought it was impossible that Africans could be using fractal geometry. — Ron Eglash

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 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

A fractal is a mathematical set or concrete object that is irregular or fragmented at all scales. — Benoit Mandelbrot

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

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

It's a product of the fractal laws that govern the world at an informational level. There is no deeper truth. — Terence McKenna

Modern humans became fixated on a collective hallucination of linear time, ignoring the fractal spirals of the surrounding universe. — Daniel Pinchbeck

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

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 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

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

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

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. — Michael Crichton

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

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

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

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

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. — 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

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

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

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. — Paul Levy

Spontaneous storms, and changes in color that were not tied to changes in wind speeds, and fractal borders, bounded infinities scrolling inside each other. We were looking at a mind thinking. A mind feeling.
The woodwind glissando of the whale's cry. — Kim Stanley Robinson

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

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

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

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

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