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 More Quotes by Benoit Mandelbrot More Quotes From Benoit Mandelbrot Bottomless wonders spring from simple rules, which are repeated without end. Benoit Mandelbrot miracle simple spring 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. Benoit Mandelbrot nature science lying Think not of what you see, but what it took to produce what you see. Benoit Mandelbrot produce thinking Regular geometry, the geometry of Euclid, is concerned with shapes which are smooth, except perhaps for corners and lines, special lines which are singularities, but some shapes in nature are so complicated that they are equally complicated at the big scale and come closer and closer and they don't become any less complicated. Benoit Mandelbrot lines shapes special A formula can be very simple, and create a universe of bottomless complexity. Benoit Mandelbrot formulas complexity simple 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 mountain circles clouds A fractal is a way of seeing infinity. Benoit Mandelbrot fractals infinity way Being a language, mathematics may be used not only to inform but also, among other things, to seduce. Benoit Mandelbrot engineering may science The theory of probability is the only mathematical tool available to help map the unknown and the uncontrollable. It is fortunate that this tool, while tricky, is extraordinarily powerful and convenient. Benoit Mandelbrot powerful tools science Many painters had a clear idea of what fractals are. Take a French classic painter named Poussin. Now, he painted beautiful landscapes, completely artificial ones, imaginary landscapes. And how did he choose them? Well, he had the balance of trees, of lawns, of houses in the distance. He had a balance of small objects, big objects, big trees in front and his balance of objects at every scale is what gives to Poussin a special feeling. Benoit Mandelbrot small-objects distance beautiful One couldn't even measure roughness. So, by luck, and by reward for persistence, I did found the theory of roughness, which certainly I didn't expect and expecting to found one would have been pure madness. Benoit Mandelbrot persistence rewards luck Self-similarity is a dull subject because you are used to very familiar shapes. But that is not the case. Now many shapes which are self-similar again, the same seen from close by and far away, and which are far from being straight or plane or solid. Benoit Mandelbrot shapes self dull There is a joke that your hammer will always find nails to hit. I find that perfectly acceptable Benoit Mandelbrot acceptable hammers nails The most complex object in mathematics, the Mandelbrot Set ... is so complex as to be uncontrollable by mankind and describable as 'chaos'. Benoit Mandelbrot chaos mathematics mankind Fractal geometry is not just a chapter of mathematics, but one that helps Everyman to see the same world differently. Benoit Mandelbrot mathematics helping world The most important thing I have done is to combine something esoteric with a practical issue that affects many people. Benoit Mandelbrot issues important people Engineering is too important to wait for science. Benoit Mandelbrot engineering important waiting 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 nomenclature numbers science A cloud is made of billows upon billows upon billows that look like clouds. As you come closer to a cloud you don't get something smooth, but irregularities at a smaller scale. Benoit Mandelbrot smooth clouds looks Think of color, pitch, loudness, heaviness, and hotness. Each is the topic of a branch of physics Benoit Mandelbrot branches color thinking
