I was arranging a 2d labyrinth IsoSurface that looks similar to architecture and erratic menger sponges:
It is a pleasing distribution of space, and it challenged me with an enigma:
If the Mandelbrot Set distant appearance is condensed into the center of the graph, is it possible to transform it into a sponge equivalent, where the Mandelbrot is isometric on the 2d plane, where the color islands are surrounded by seas of zeros, where i can adjust the sea to land ratio and the isthmus geometry?
I started graphing the mandelbrot set on every square of the sponge maze, so that squares merge over it's neighbours and multiplies the values of n mandelbrot sets from a spherical multiplication range surrounding the center of every square.
The result was an equivalent of the mandelbrot set which is isometric in 2d and 3d space rather than on the origin and where the edges of the mandelbrot are multiplied so that round zones fold over into tree patterns and provide inverse round tree conch shell objects which are a new world which descends into ever deeper levels of abstration and where n 3d fractals formulas can be combined with each one centered on a cubic sphere of influence within the labyrinth, and the circles also divide into simpler sine-cosine wave structures and hyperboles that bend the trees around.
The result was a spongey equivalent of the mandelbrot set. And then i wished to also fold circles into the square 2d isosurface to have a combination of a Mandelbox and a Menger Sponge...
It was all very fun, and transformed into 3d space very effectively to make new kinds of 3d visualisations, and i became a very famous mathematician. At that moment, my dream was interrupted by a car doing wheelies in the parking lot and my spongedelbrot and boxdellisponges formulas vanished from my memory.
If you mathematicians that can do mathematics consciously, can help me to travel again to the worlds of spongedelbrot i would be very happy. here is an isosurface labyrinth for graphics engines, the idea is to arrange them with occult hyeroglyphs of paranormal font sets, and xenoform monster geometry on the walls, and in the labirynth you will run away from floating hungry jellyfish trees with gelatine phylogeny arms, here is the file.
this runs in openscad program for 3D engineers:
labyrinthIsoSurface();
ridgeDensity = 200;//higher values compress the random oscillator at higher frequency
brickDensity = 0.43;//regulates the difficulty of maze
mixIntensity= 0.1;
mazeSize = 100;
module labyrinthIsoSurface (){
for( j = [ 1 : mazeSize ])
for( i = [ 1 : mazeSize ])
{
li = lfo(i*ridgeDensity)*532.154;//random lfo values
lj = lfo(j*ridgeDensity)*451;
xc= (lfo(j*mixIntensity+li) + lfo(i*mixIntensity+lj))*.25+brickDensity;//
//xc= (lfo(li) + lfo(lj))*.25+.40;//run this version to see simple version of maze
rd = round(xc)*55;
//echo(xc);
if (xc > .5) // if isosurface is small, build wall cube
{
translate( [j ,i, 0])
cube(1);
}
}
}
function mod(a,m) = a - m*floor(a/m);
function lfo(xx)= mod(abs((sin(floor(xx))*0.01246)*32718.927),1.0)*2.0 - 1.0 ; //erratic sin
//low frequency oscillator function similar to synthesizer robot sound like R2D2