I drew these corals with mathematical equations | Hacker News Reader

I drew these corals with mathematical equations

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167 pointsr_singh30 comments

If you think that's cool you'll like this guy's equations too. Written in GLSL so they run in your browser in real time as well. https://x.com/zozuar

And, of course there's also the classic Shadertoy https://www.shadertoy.com/results?query=&sort=love

Doing this inside the character limit is blowing my mind rn

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.

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.

It’s non-stop uncanny valley.

Perhaps because biological creatures themselves can exhibit complex shapes and patterns through simpler mathematical principles like fractals and cellular automata

Came here to say exactly that. Fascinating, but deeply unnerving for some reason.

Obligatory demoscene links for anyone continuing down the rabbit hole: https://nanogems.demozoo.org/, https://www.pouet.net/.

Very cool! This reminds me of the guy 3D modeling a selfie-girl with math equations: https://www.youtube.com/watch?v=8--5LwHRhjk

Indeed, Inigo Quilez is "the guy" for this kind of stuff. He co-created ShaderToy and has worked on effects and modeling for multiple Pixar films.

My favorite video of his is Painting a Landscape with Maths.

https://www.youtube.com/watch?v=BFld4EBO2RE

He deserves to have at least as many subscribers as other math YouTube channels like Verisatium and 3Blue1Brown.

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

It is one big equation, he just isolates each piece to better explain it

Somewhat related (pops up here from time to time): How to draw a butt in mathematica. https://mathematica.stackexchange.com/questions/66538/how-do...

Previous discussion: https://news.ycombinator.com/item?id=34257837

Obligatory nitter link: https://nitter.net/naderi_yeganeh/status/1690296100496838656

More images in https://twitter.com/naderi_yeganeh

In another xtter, he posted a link to a blog that explains how he finds the equations. It's a general discussion with example, not a specific discussion of the corals. https://blogs.scientificamerican.com/guest-blog/how-to-draw-...

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...

https://www.generativeart.com/on/cic/GA2009Papers/p17.pdf

Here's a quine in a similar fashion: https://en.wikipedia.org/wiki/Tupper's_self-referential_form....

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.

he's got a lot of these

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 looks very similar to Apple's "Drift" screensaver from macOS Catalina [0], which is also calculated in real time.

[0] - https://www.youtube.com/watch?v=7WXzRhebz1g

It looks a lot like a H. magnifica anemone’s tentacles.

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.

Way too many parameters to be interesting. Talk about fitting an elephant.

Very cool!

finally a twitter user that is:

a real person

not posting about politics or crypto (which probably refutes the first criteria)

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'.

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