I saw this blog post by an extremely talented programmer, and was suprised (as he was) to find that there was a natural symmetry to the patterns he was describing. However, in digging into his code, I found that it was not actually symmetrical, but he had just made a very understandable typo which introduced this artificial symmetry.
Working with these equations, I found that the surfaces generated by them were gorgeous, and that the surface appeared to be differentiable with respect to every one of the input paramters. In my experience, this is rare for a multi-dimensional equation.
Just iterating around a bit, I found that the most “interesting” cases all happened at a relatively uniform distance from the origin of the parameter space. I then thought about how I could generate a nice video of a tour of the parameter space, and my mind lept to an orbit. I created the software to output a gif of the generated curve for a given circular or eliptical orbit around the center of the parameter space.
I then made many of these gifs, all of which share a starting and ending position in the parameter space. This means that played in any sequence, the gifs will make a beautiful pattern that appears continuous, infinite and quazi-random.
This work insipred me to do more code-art for the sake of the art, rather than the sake of the code.
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