Benoit Mandelbrot Shapes Quotations

There are very complex shapes which would be the same from close by and far away.

If you look at a shape like a straight line, what's remarkable is that if you look at a straight line from close by, from far away, it is the same; it is a straight line.

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.

Everything is roughness, except for the circles. How many circles are there in nature? Very, very few. The straight lines. Very shapes are very, very smooth. But geometry had laid them aside because they were too complicated.

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.

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.

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.

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.