Doctor Benoit Mandelbrot defined what is a fractal on page 15 of his seminal book “The Fractal Geometry of Nature” where he stated:
“A Fractal is by definition a set for which the Hausdorff Besicovitch dimension strictly exceeds the topological dimension”. (*)
…but then I’ve heard that he later changed his mind.
I have the book. I’ve read the book. No, I don’t understand the book. But I must be an intellectual because I’ve read the book.
Q: What does the “B” in “Benoit B Mandelbrot” stand for?
A: “Benoit B Mandelbrot”
While were on the topic of fractals*, how do people produce stuff like this: Mandelbrot fraktaler super deep 2 2^4750 - YouTube
I written a few Mandelbrot explorers in my time. In fact, whenever I want to learn a new language, my go to first problem is the Mandelbrot set because it lends itself to concurrent computations so well. However, even disregarding the arbitrary precision needed for these zoom levels, with any of the programs I have written, it would take a ridiculously long time to run.
I’m aware of some of the obvious optimizations like rather than looking for absolute value greater than 2, look for a squared value greater than 4, so you don’t have to do a square root. But even with these kinds of optimizations, there is still no way my Core i7 could get there in any reasonable amount of time.
So my question is: is this stuff as it seems or is there some other kind of trickery going on?
*Seems like this question has been answered and my related question is probably not deserving of it’s own thread.
What do you consider a ridiculous amount of time? Although the description doesn’t say, I’m sure the animation took a long time to render; perhaps weeks.
The link goes to a page which describes an algorithm that runs much faster than the standard ones at very deep zooms. It’s fairly clever–it computes one reference point using arbitrary precision arithmetic, while nearby points are computed using differences (which are small and can use native CPU arithmetic).
How do you know that isn’t already true?
Simulating reality will always be less efficient than reality, even with quantum computers. We could only simulate a small part of the Earth with a quantum computer the size of Earth. So it might be a while before we have truly compelling simulations. Maybe one day we’ll disassemble Jupiter and convert it into a computer.
Consider, too, that fractal images have been all over the place since the 1970s. Now consider the difference in computing power between then and now.