Introducing Fractals Quotes

“The word “fractal” was coined in 1975 by the Polish/French/American mathematician, Benoît Mandelbrot (b. 1924), to describe shapes which are detailed at all scales.”
― Nigel Lesmoir-Gordon, Introducing Fractals: A Graphic Guide

“Arthur C. Clarke thinks that it may be just a coincidence, "but", he writes, "the Mandelbrot set does indeed seem to contain an enormous number of mandalas or religious symbols, which are found in ecclesiastical designs-such as stained glass windows, and particularly in Islamic art. We find many forms like the Paisley pattern echoing the Mandelbrot set centuries before it was discovered!”
― Nigel Lesmoir-Gordon, Introducing Fractal Geometry

“The abstract, curvilinear motifs of ancient Islamic decorative art found in mosaics and carpet design appear again and again at all scales of magnification on the boundary of the Mandelbrot set.”
― Nigel Lesmoir-Gordon, Introducing Fractal Geometry

“We know that different regions in the brain process shape, colour, and motion. Benoit Mandelbrot has hypothesized that perhaps there is a specific circuit in the brain to deal with fractal complexity.”
― Nigel Lesmoir-Gordon, Introducing Fractal Geometry

“Nature deals in non-uniform shapes and rough edges. Take the human form. There is a certain symmetry about it, but it is, and has always been, indescribable in terms of Euclidean geometry.”
― Nigel Lesmoir-Gordon, Introducing Fractals: A Graphic Guide

“The rare scholars who are nomads-by-choice are essential to the intellectual welfare of the settled disciplines.”
― Nigel Lesmoir-Gordon, Introducing Fractal Geometry

“Spectral analysis of music from classical to nursery rhymes has revealed a remarkable affinity with patterns in nature, in particular fractal distribution called 1/f noise, which is found in the sound of a waterfall or waves crashing on the beach.

1/f noise lies midway between the total chaos of white noise..

..and overly-correlated brown noise.

All music from Bach to the Beatles, even birdsong, is characterized by 1/f noise, displaying the same dynamic balance between predictability and surprise, between dull monotony and random discord. Seen in this light, music is essentially a simulation of the harmony in nature.”
― Nigel Lesmoir-Gordon, Introducing Fractal Geometry

“Fractal shapes were being expressed intuitively by artists long before they were recognized in science. Self-similar patterns appear in Celtic artefacts, like the spirals and circles within circles of the exquisitely crafted illuminated pages of the early 9th-century Book of Kells and the Densborough mirror made in the 1st century A.C. Mathematical awareness, particularly fractal awareness, reveals itself in the art of the Romans and the Egyptians, and in the work of the Aztec, Inca and Mayan civilizations of Central and South America. Shapes highly reminiscent of the Koch curve were used to depict waves by the Hellenic artist in a frieze in the ancient Greek town of Akrotiri.”
― Nigel Lesmoir-Gordon, Introducing Fractal Geometry

“In Mahayana Buddhism, the fractal nature of reality is illustrated in the Avatamsaka Sutra by the metaphor of Indra's net, a vast network of precious gems hanging over the palace of the god Indra, so arranged that if you look at one you see all the others reflected in it.”
― Nigel Lesmoir-Gordon, Introducing Fractal Geometry

“Zooming into the boundary of the M-set, we find smaller and smaller island molecules, surrounded by increasingly intricate circular patterns, evocative of Oriental art, particularly in the meditative designs of Buddhism known as mandalas.”
― Nigel Lesmoir-Gordon, Introducing Fractal Geometry

“The process of rotating, stretching, and moving is called an affine transformation.”
― Nigel Lesmoir-Gordon, Introducing Fractal Geometry

“Real-world images have redundant information. Tree bark has repeating patterns with small variations.”
― Nigel Lesmoir-Gordon, Introducing Fractal Geometry

“Fractal image compression can even guess, by interpolation, what lies outside the frame of a picture.”
― Nigel Lesmoir-Gordon, Introducing Fractal Geometry

“Self-similarity on all scales is a key factor in understanding and describing nature's phenomena.”
― Nigel Lesmoir-Gordon, Introducing Fractal Geometry

“Research employing fractal rules has revealed a three-quarter power law even in the circulatory system.”
― Nigel Lesmoir-Gordon, Introducing Fractal Geometry

“We are fractal. Our lungs, our circulatory system, our brains are like trees. They are fractal structures.

Fractal geometry allows bounded curves of infinite length, and closed surfaces with an infinite area. It even allows curves with positive volume, and arbitrarily large groups of shapes with exactly the same boundary. This is exactly how our lungs manage to maximize their surface area.

Most natural objects-and that includes us human beings-are composed of many different types of fractals woven into each other, each with parts which have different fractal dimensions. For example, the bronchial tubes in the human lung have one fractal dimension for the first seven generations of branching, and a different fractal dimension from there on in.”
― Nigel Lesmoir-Gordon, Introducing Fractal Geometry

“Brownian motion, the movement of a tiny smoke particle due to the constant bombardment of millions of invisible air molecules, traces a fractal path with dimension close to 2.”
― Nigel Lesmoir-Gordon, Introducing Fractal Geometry

“What we find is highly sensitive dependence to initial conditions, producing phase transitions.

Once a critical threshold is passed, the fire spreads outwards, the disease becomes an epidemic, the material magnetic.”
― Nigel Lesmoir-Gordon, Introducing Fractal Geometry

“Period-doubling is a general principle of nature.”
― Nigel Lesmoir-Gordon, Introducing Fractal Geometry

“The signature of chaos is the fractal attractor-fractals are the patterns of chaos”
― Nigel Lesmoir-Gordon, Introducing Fractal Geometry

“Art is about those things which we do not always immediately recognize or understand. The artist helps us to see things more clearly, revealing previously hidden patterns to us. Art is fractal. Art reflects and expresses the fractal nature of our conscious perceptions of the world, as interpreted by our fractal brains.”
― Nigel Lesmoir-Gordon, Introducing Fractals: A Graphic Guide

“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, Introducing Fractals: A Graphic Guide

“Detecting Cancer The surface structures of cancer cells are crinkly and wrinkly. These convoluted structures display fractal properties which vary markedly during the different stages of the cancer cell’s growth. Using computers, mathematical pictures can be obtained, which reveal whether or not cells are going cancerous. The computer is able to measure the fractal structure of cells. If cells are too fractal, it spells trouble. There is something wrong with those cells.”
― Nigel Lesmoir-Gordon, Introducing Fractals: A Graphic Guide

“The Mysterious Brain One thing we can say with certainty about the brain is that it is a very fractal piece of kit! It has an obvious fractal structure. You have only to look at it to see that. It is very crinkled and wrinkled and highly convoluted, as it folds back and back on itself. It is deeply ironic that this remarkable organ, which is the seat of the mind, and which either created or discovered (we don’t know which) the mathematical rules on which it and the entire universe turns, cannot explain or understand its own functioning. If we understood how our brains worked, would we not have achieved those dizzying heights conjured up by Stephen Hawking in A Brief History of Time – would we not, then, “know the mind of God”? Understanding how our brains function is probably the greatest challenge facing the scientific community at this time. Fractal geometry is at the leading edge of research in this area.”
― Nigel Lesmoir-Gordon, Introducing Fractals: A Graphic Guide

“Dimensional Magic We are fractal. Our lungs, our circulatory system, our brains are like trees. They are fractal structures. Fractal geometry allows bounded curves of infinite length, and closed surfaces with an infinite area. It even allows curves with positive volume, and arbitrarily large groups of shapes with exactly the same boundary. This is exactly how our lungs manage to maximize their surface area.”
― Nigel Lesmoir-Gordon, Introducing Fractals: A Graphic Guide

“More Phase Transitions This principle applies just as much to the spread of infectious diseases or magnetic polarity as to forest fires. It is essentially the same process unfolding.”
― Nigel Lesmoir-Gordon, Introducing Fractals: A Graphic Guide

“Forest Fires: the Fractal Boundary Imagine a plantation of evenly spaced trees on a very hot, dry day. As the temperature soars, the odd leaf or twig ignites, sending a whole tree up in flames. This is an essentially random process – the factors involved are beyond our powers of prediction. But once a tree is in flames, the fire easily spreads to neighbouring trees, and this process can now be modelled with iterative techniques.”
― Nigel Lesmoir-Gordon, Introducing Fractals: A Graphic Guide

“Nature finds the same solution to many different problems, like how to drain water from the land into the oceans, and how to get blood from our hearts to our fingertips and back again. And the templates that nature uses are fractals. Clouds look the same at all scales. It is impossible to determine the size of a cloud from a photograph of it.”
― Nigel Lesmoir-Gordon, Introducing Fractals: A Graphic Guide

“This is the fundamental characteristic behind the growth of all complex organisms. The same forms recur in many different circumstances, in different materials both organic and inorganic, on a vast range of scales. A small part of our circulatory system looks like the whole. It looks like a tree, like an estuary, like a stream-bed.”
― Nigel Lesmoir-Gordon, Introducing Fractals: A Graphic Guide