Benoit Mandelbrot Quotes

A formula can be very simple, and create a universe of bottomless complexity.

My take is that the kind of complexity which says we can always generate complexity from simple interactions following for example rules.

There’s so much distance between the fundamental rules and the final phenomenon, that it’s almost unbelievable that the final variety of phenomenon can come from such a steady operation of such simple rules.

And so from that, I've always been fascinated with the idea that complexity can come out of such simplicity.

The beauty of compounding iterative algorithms - evolution, fractals, organic growth, art - derives from their irreducibility.

I think the next century will be the century of complexity.

There are only patterns. Patterns on top of patterns, patterns that affect other patterns, patterns hidden by patterns, patterns within patterns.

No one disputes that seeming order can come out of the application of simple rules. But who wrote the rules?

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.

...All the wonders of our universe can in effect be captured by simple rules, yet ... there can be no way to know all the consequences of these rules, except in effect just to watch and see how they unfold.

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

Entropy theory is indeed a first attempt to deal with global form; but it has not been dealing with structure. All it says is that a large sum of elements may have properties not found in a smaller sample of them.

I'm interested in complexity, in the mathematical sense, as well as the idiomatic sense. The idea of emergence - that it's possible for complex patterns to arise out of many simple interactions - is fascinating.

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

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.

The world is deterministic, but it's chaotic and emergent.

Closed systems run down and get more chaotic over time. Always get better by being 'open' to outside energy and templates of better ways to function.

An exquisitely complex shape now known as the Mandlebrot set has been called the most complex object in mathematics.

Anybody can find infinite Mandelbrot figures in his navel.

We get to the point then with modern science where you could almost say that modern science is the art of describing those systems so crude in their structure that they are not subject to temporal variables.

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

Every you, every me. Fractals. Fractures.

Disorder can play a critical role in giving birth to new, higher forms of order.

When people ask me what's my field? I say, on one hand, a fractalist. Perhaps the only one, the only full-time one.

Now, as Mandelbrot points out, ... Nature has played a joke on the mathematicians. The 19th-century mathematicians may not have been lacking in imagination, but Nature was not. The same pathological structures that the mathematicians invented to break loose from 19th-century naturalism turn out to be inherent in familiar objects all around us.