I finally had the time to go and watch the movie Doctor Strange and I was mesmerized by the special effects they used and how they used some great mathematical techniques there. When I say this, it doesn’t refer to just some random geometrical patterns, but at great interesting fractals (Mandlebrot sets) and some of Escher’s art and patterns.
Here are just a couple of images, but they don’t give much about the greatness of how it really looks in 3D:
Here are a couple of words about the work behind it from the creators:
‘There’s the whole set bending and moulding, cloning and reconfiguring itself, but then there’s also the Mandelbrot pattern, which is the mathematical formula that creates these crazy patterns and adds the fractured world aspect to it’, adds Mark Wilson (VFX Supervisor). ‘Once we had animated all of these assets, our FX team then placed additional Mandelbrot sponge fractal patterns inside it, using Houdini to drive a proprietary Arnold procedural iso surface shader at render time to give us a mathematical organic growth. That was really cool; it was all new to us!’
The mathematical inside into the Mandelbrot set is not very straight forward. This is one of those topics which looks absolutely incredible, but is very hard to explain what it actually represents (at least for me at this point). The definition is not extremely helpful at this stage, by here it goes: the Mandelbrot set is the set of complex numbers c for which the function does not diverge when iterated from , i.e., for which the sequence , , etc., remains bounded in absolute value. The process of how mathematicians or artists create those beautiful representations from this definition is even more interesting.
Mandelbrot set images may be created by sampling the complex numbers and determining, for each sample point c, whether the result of iterating the above function goes to infinity. Treating the real and imaginary parts of each number c as image coordinates, pixels may then be colored according to how rapidly the sequence diverges, with the color 0 (black) usually used for points where the sequence does not diverge.
Images of the Mandelbrot set exhibit an elaborate boundary that reveals progressively ever-finer recursive detail at increasing magnifications. The “style” of this repeating detail depends on the region of the set being examined. The set’s boundary also incorporates smaller versions of the main shape, so the fractal property of self-similarity applies to the entire set, and not just to its parts.
I consider that studying this part of mathematics is not as straight forward as we might think and seeing it represented (even just visually) in a movie, which could become incredibly popular, is quite beneficial for mathematics as a whole. Now, as a teacher of mathematics, I feel like this could be one of those great examples of mathematics used in different type of jobs and how interesting and beautiful it can be.
I totally advise you give it a try to this movie if you haven’t. Also, because of the visual effects it has, this is a definitely 100% must see in 3D movie. Here is the trailer, just in case:
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Don’t forget that maths is everywhere! Enjoy!