Press 1 or 2 for example settings, or chose k by selecting a point on the Mandelbrot set. You can either see the full 3D slice at either Re(c) = Re(k) or Re(z0) = Re(k), Or press S to toggle slicing the top of it to also show the 2D slice where Im(c) = Im(k) (so c = k) or Im(z0) = Im(k) (z0 = k). Toggle between setting z0 and c with J/M Then space to do the thing (after choosing the resolution, for scratch use 2 or 4, but 0.5 on turbowarp.
Mandelbrot image by Wolfgang Beyer. @Yeah-Hello asked me to make this. The idea to show the mandelbrot set when you chose the point was from @rams906 I have to admit that I don’t fully understand the sdf for this, but I have managed to get it working after many failed attempts. The actual shape is simple though, it is based around function Z^2 + c, you start with: Re(Z0) = x Im(Z0) = y Re(c) = z Im(c) = w Then iterate: Z1 = Z0^2 + c Z2 = Z1^2 + c Z3 = Z2^2 + c etc. If Z stays small, then (x, y, z, w) is in the set, otherwise if it diverges to infinity it is not. Of course, you can’t comprehend the 4D shape, so the rendered shape is a “3D slice” with a constant x/y/z/w. The Mandelbrot set is a 2D slice when x and y are zero, so the initial value of z is zero, every 2D position is a complex value of c. The Julia sets are 2D slices at constant values of z and w. For any Julia set, c is a constant, and every 2D point is the initial z. The first preset is the 3D slice where Re(Z0) = 0, and I sliced off the top half so you can see the 2D slice where Im(Z0) = 0, hence, the Mandelbrot set appears.
