Fractals Quotes

All high mathematics serves to do is to beget higher mathematics. ~ Ashim Shanker

The best thing we can do is give students the tools for constructing their own identities - powerful new tools like African fractals - and then just get out of the way. ~ Ron Eglash

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

It has been said that the three great develpments in twentieth century science are relativity, quantum mechanics, and chaos. That strikes me the same as saying that the three great developments in twentith century engineering are the airplane, the computer, and the pop-top aluminum can. Chaos and fractals are not even twentieth century ideas: chaos was first observed by Poincare and fractals were familiar to Cantor a century ago, although neither man had the computer at his disposal to show the rest of the world the beauty he was seeing. ~ Robert L. Devaney

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

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. ~ Sharon Weil

Every you, every me. Fractals. Fractures. ~ David Levithan

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

If you take your thumb and your index finger and look right where they meet - go ahead and do that now - and relax your hand, you'll see a crinkle, and then a wrinkle within the crinkle, and a crinkle within the wrinkle. Right? Your body is covered with fractals. ~ Ron Eglash

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

Smooth shapes are very rare in the wild but extremely important in the ivory tower and the factory. ~ Benoit Mandelbrot

...A certain amount of clutter is expected. Hell, you find it everywhere. Cyphers on cereal boxes, fractals in sidewalk cracks, dead cats who don't understand why you're not paying attention to them-- Why are you looking at me like that? ~ Shukyou

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

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. ~ Nnedi Okorafor

I conceived and developed a new geometry of nature and implemented its use in a number of diverse fields. It describes many of the irregular and fragmented patterns around us, and leads to full-fledged theories, by identifying a family of shapes I call fractals. ~ Benoit Mandelbrot

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

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. ~ David Levithan

Yes, fractals are what I want to find in my music. ~ Gyorgy Ligeti

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. ~ Benoit Mandelbrot

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

God loves fractals!) ~ Daniel Keown

Humanity has known for a long time what fractals are. It is a very strange situation in which an idea which each time I look at all documents have deeper and deeper roots, never (how to say it), jelled. ~ Benoit Mandelbrot

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

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

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 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. ~ David Foster Wallace

There is no singular 'reason' why Africans use fractals, any more than a singular reason why Americans like rock music. Such enormous cultural practices just cover too much social terrain. ~ Ron Eglash

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

I need to tell you a story.'

What about?

Zachariah, Zachariah, my foundling boy. 'A boy. A boxer, a fighting man. A brother. No. About brothers, sisters. Foundlings, laid-in-the-streets. Fights, fighting. A boy, it all begins with the boy. My love. A wolf. Peter and the Wolf! Oh dear! I am very crazy! Let me - I must tell you this story.'

Why?

'I'm frightened.'

Of?

'Fractals. Patterns.'

Ah, says the fish, looking at Rachel with his wise eyes. Chaos!

'Yes,' thinks Rachel. 'Chaos. Fearful symmetry.'

Go home, says the fish, flipping over, flashing in light, and diving down into the great blue sea. ~ Emma Richler

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

I find enough mystery in mathematics to satisfy my spiritual needs. I think, for example, that pi is mysterious enough (don't get me started!) without having to worry about God. Or if pi isn't enough, how about fractals? or quantum mechanics? ~ Tom Lehrer

Rachel believes in it, the laws of of pattern formation and how they are universal: whatever she sees, crystallizing, a landscape of fractals, of emergence and symmetry, her world falling happily into shape where he must forge it, a pioneer of industry, sooty and scarred. For Rachel Wolff, quite simply, there are patterns everywhere, she can't help it; she is an illustrator, naturalist, cartographer - and her eye, a kaleidoscope. ~ Emma Richler

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

The discovery of the fractals had proven that in a world of chaos, there is a way to understand the natural world by using something as definite and precise as values and numbers. Things and events that were beyond our understanding slowly emerge as distinctively clear as figures and images, leaving no room for mysteries and ambiguities, making the universe more understandable in the eyes of people. With this, it presents a definite point of view in the way complex things are to be observed, which would represent irregularities and open up new paths for discovery. ~ Tim Clearbrook

You were, are
cactus tourism.

meeting you: granular

fractals borrowed from oceans. ~ Virginia Petrucci

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

Any detail can be magnified to reveal even more detail ad infinitum. The technical term is "infinite complexity." Fractals are the theological equivalent of what theologians call the incomprehensibility of God. Just when we think we have God figured out, we discover a new dimension of His kaleidoscopic personality. ~ Mark Batterson

I just toured around looking for fractals, and when I found something that had a scaling geometry, I would ask the folks what was going on - why they had made it that way. ~ Ron Eglash

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

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

Now in the 1980s, I happened to notice that if you look at an aerial photograph of an African village, you see fractals. And I thought, 'This is fabulous! I wonder why?' And of course I had to go to Africa and ask folks why. ~ Ron Eglash

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