There's something in many of those those Zozuar animations that trigger what I'm sure is a primal fear with me. Fascinating stuff but some of it is terrifying.
Perhaps because biological creatures themselves can exhibit complex shapes and patterns through simpler mathematical principles like fractals and cellular automata
That's what I was thinking as well -- these are equations that generate colors in 2D space, so essentially pixel shaders, but for this particular effect I wonder if it would be simpler with some geometry shaders, and have a 3D engine take care of the shadows.
not quite the same thing. piecing together parts with individual equations, like a mosaic, not the same as modeling the whole thing with a set of huge parametric equations
L-Systems, in my opinion, are much more simple, expressive and easy to understand, and actually can result in very similar structures. There's also the CFDG/Context Free (curiously by Chris Coyne) system which allows grammar-based inference which produces structures sembling bioforms, also very straightforward. Also continuation of this reasoning is Structure Synth...
I don't think this is quite the same fashion, the original post looks like the geometry is being generated by the equations while Tupper's formula directly stores a bitmap image in the coordinates.
Misleading name. It's not self-referential at all; it's just a simple bitmap renderer written in mathematical notation. The actual bitmap is stored separately.
it seems to me like he's deriving the equations from images that he finds, then using the equations to generate new images with a stroke of randomness.
That would be far more impressive if true. The equations while having a number of magic numbers also don't have that many parameters, so it would seem difficult to find such equations to fit well to images.
this is great and all but the way of mathematical equations isnt quite the way of the computer. its kinda like hardcoding with magic numbers. on the computer you want to model the processes that makes the coral and then let the computer unfold it and hopefully it produces your coral. more interestingly, it will produce other shapes nature hasnt thought of yet.
That's the basis of ancient greek mathematics which used the world as the model of its mathematics. So if twitter was around in the ancient greek world: 'OP derived these mathematical equations from these corals'.
And, of course there's also the classic Shadertoy https://www.shadertoy.com/results?query=&sort=love