A computer security pioneer, Michael Mandelbrot, developed the first numerical expression algorithm and the first computer program that uses that algorithm, called a fractal program. In 2007, he published a book called The Man Who Knew Infinity. The book covers Mandelbrot’s life and career from 1977 through today.
Are the numbers in The Matrix real?
Yes! Mandelbrot is a real person, the character in the film is based on him, although the actor was not actually the mathematician, but a member of Mandelbrot’s research group that studied fractals. The real math involved was just making it look real.
You also work with fractals. Can you explain a bit more about how fractals work?
Fractals are very difficult for us to describe. They are such a huge part of our everyday experience that the simplest explanation is much too simplistic. To understand fractals, we need something that’s like the simplest description possible: it’s the most basic set of shapes and relations that describe nature and everything in it. The fundamental physical laws that govern our physical world are these shapes and relationships. Fractals describe those laws. Here are a couple of example: The topology of a 3d space is a 3-dimensional version of the geometry of our world — the triangle is a 3-dimensional version of our four-dimensional (x, y, z) grid. The geometry underlying gravity is 3-dimensional fractal geometry. One of the main mathematical concepts behind fractal geometry is the concept of a “fractal wave”, a space-like wave that is composed of very simple shapes with an infinitely repeated pattern. There are two main fundamental types of fractals — an infinite dimensional form called a “fractal number” (or F), and a form called a “regularized” F (or RE). In the RE form, the 3-dimensional form is made of regular, compacted, finite, multiples of a certain size. This form is called a “form of the Fibonacci numbers”. The regularized form is made of a similar finite number of smaller, compacted, multiples of the F shape, like Fibonacci numbers. These forms are called “formal” fractals. Here are a couple of example, where we take different forms of the Fibonacci Numbers:
F = (-1, 0, -1),
RE = (-2, +1, 2),
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