It’s a pretty cool program that operates along the lines you are describing although it uses a visual tree designer to wire up components that transform x, y, z and other coordinates. I have what is now quite an old version and I love playing with it from time to time and just browsing the oddities it can make.
Wenger is I think most famous for MetaSynth (which I also have a very old version of).
Neat! Looks like he does a lot of this kind of stuff: Hamid Naderi Yeganeh - Wikipedia
Inigo Quilez’s YouTube channel also has some interesting videos on more conventional ways of drawing things with maths…
Without any zoom, here’s a rainbow like Mandelbrot dragon. I came up with the math filter which is based on angular decomposition. Any of this could be zoomed into. You can try my fractal software on itch and make these for yourself. If anyone wants to build in a math art function, I’d love to add it with you.
It looks much better at full resolution and is faster than this gif demonstrates but you get the picture.
It also reminds me of the shader stuff some twitter users used to post:
Looks great!
I am putting final touches on an epic-length branching narrative, trying to find publishers for collections of poetry, finishing up a three-year project at work, and trying to convince myself to finish my end of the world trilogy, an absurdist horror about two warring fast food taco places. I’d love feedback on Ashes of a Dark Harvest if anyone is interested in play-testing before the cover artist is done with her work.
I love fractals!
I do too. I sank a whole bunch of time in the book “Fractal Programming in Turbo Pascal” by Roger T. Stevens. It is so old by tech standards (1990) that the books source came on a 5 1/4” floppy. I still own it but only have a 3.5” floppy reader.
I wish I could see that dragon… And yes, fractals are awesome… among other things, I want a Koch Snowcube paperweight, Apollonian spheres stress ball, and a level 4 menger sponge made of 16mm d6s as a table/shelving unit… and pas reliefs of numerous views of the mandlebrot set.
ArtMatic does sound like a cool bit of hardware, but even if I had a Apple PC and could afford it, I’d worry it wouldn’t be very accessible.
Also, that photorealism from maths bit reminds me of the Everything Formula that was highlighted in a Numberphile video:
Also, here’s a wikipedia link relevant to the above linked video:
Also, I’m pretty sure I’ve encountered a formula before that when graphed draws the Batman Emblem… Though, when you think about it, all static computer images are ultimately the result of a function mapping the x and y-coordinates of a pixel’s location to the r, g, and b-coordinates of the pixel’s color… And all sound waves are the sum of some set of pure sine waves, so it’s not that hard to believe that, given enough parameters, any image can be represented as a function… Of course, there’s probably a point where just listing the color for every pixel takes up less information than the formula for the function… Though, doesn’t some data compression rely rely on summing just the first n sine waves of a fourier transform instead of the infinite number of sine waves of the full transform? This is getting into maths where I kind of understand the concepts, but don’t really understand the nitty gritty of actually calculating it by hand or writing a program to do the calculations.
There is a way you could see it by touch. Early fractal renderers use what is called an escape orbit to create a false color spectrum. It is the number of iterations it takes for the point in the set to escape and thus not be part of the solution set. I’ve often wanted to visualize this in 3-d because that same iteration count could become an elevation and if you print the fractal in the rectangular region using elevation instead of color, you could make something tangible using a 3d printer.
If you know the usual Mandelbrot shape, this is a lot like two of those back to back so it the body of the two Mandelbrot “bugs” are like two giant eyes looking at you, and it’s using a rainbow color ramp so all the surrounding fades are repeating rainbows (hmm, except they’re wobbly bands running around the fractals instead of like waves lapping at the shore of the fractals). And then from the GIF it looks like there are waves of red/green/blue rotating through the right “eye” from the center of the left edge, and also all the rainbows slowly rotate around the eyes as well. Very trippy.
Hooray for physical things!
That’s the kind of thing I was hinting at when I said I want bas reliefs of the Mandelbrot set, using how fast points outside the set fly off to infinity as elevation instead of coloration… Sadly, while software to generate static images and animations of fractals are common, at least for the better known fractals, I’m not aware of any tools that will output an stl of fractals, and while home 3-D printers have come down a lot in price, they’re still a pretty penny for any halfway decent unit, but the rise of home printers has lead to the 3D print shop industry kind of imploding, so even if there was a fractal generator with an export as stl option, getting it printed can be a challenge for those who don’t own their own printer.
Though, the above description of the mandelbrot dragon has me curious how the Mandelbrot set would be altered if one were to take the absolute value of the real part, the imaginary part, or both… Or how the mandelbrot set would look through a kaleidoscope.
Also, a Sierpinski Carpet as an area rug would be cool… Also, I find myself wonder how the Sierpinski Carpet, Sierpinski Triangle, and other such fractals would look if instead of the standard two tone depiction, you used a different color to the area altered at each iteration.
I finished a new album, now I just gotta wait for the weekend to tell people it’s published. 
I don’t know where you live but where I live the public libraries have fantastic 3d printers. They also have a web portal where print jobs can be submitted and picked up when printed. The library in my downtown city, medium sized city by city standards with around 415,000 folks, has a tech lab with a bunch of cool stuff for media creation, duplication, and 3d printing.
I will make it a priority to make an export to stl in my fractal generator. It would please me to the end of the earth knowing I could help bring the joy this software has given me to another group. It is why I made it in the first place. Just like sorrow shared is halved, joy shared is doubled.
Wow, that’s really cool! What a nice idea for a library.
My fractal generator, Fractal, now exports fractals to .STL files. Here is a sample. I had all the data already, everything. I just had to turn the height data (colors) into a triangular watertight mesh. It looks like it needs some work to normalize the height but it is still cool.
Honestly, I don’t even know if this small town has a public library or how to find out, but even if there is a local library with such services or a local maker space, getting there would be a challenge as where I live has no pedestrian access, ther is no local mass transit, the local paratransit sucks(the biggest hurdles being a 2 shopping bags per rider limit and assuming that because I’m blind, I need a sighted guide, so they won’t let me ride alone… ableism sucks, but it’s extra bad when you have to deal with it from a service meant to get around part of the ableism problem), and I don’t have anyone I can reliably call for a ride. I do all my shopping online and get my groceries delivered not out of convenience, but out of necessity(though honestly, I’d probably do grocery delivery out of convenience even if the 0.8 mile walk to the nearest grocery store wasn’t suicidally dangerous for someone with working eyes, but it would be nice to live somewhere I could, on a whim, safely walk to a bus stop, hop a bus to a decent local mall and spend a few hours walking around and window shopping at my own pace.
Sorry if I’m being a bit of a downer and don’t have anything new to share from my own creative endeavors.
Continuing my programmatic art, I decided to try my hand at making some graphics that might be used if I ever tried my hand at making a GUI for atile matching puzzle game. Made two blocks so far, one intended as a red circle the other as a purple asteroid, both with a animated gradient. Decided to make them 128*128 pixels with a 4 pixel black border and sharp corners. Fairly confident I got the red as I wanted since I’ve down circular gradients many times, but I’m less confident I got the purple right, especially with the animation.
https://sightless-sanctuary.net/Graphics/Programmatic/PuzzleBlocks/purple.png
Also, after several large pieces that required tens of gigabytes of disc space for generation and end results that were hundreds of megabytes, it was nice to have something small enough I could probably run it on a pentium-era machine no problem.
