i have a small problem where my mandelbrot set is represented as a heightmap matrix, when every cell contains the number of iterations it took a single point to reach infinity or less.
in the end a 3d model is printed. my problem appears when i zoom rapidly and i begin to see that the entire set floats(because the number of iterations gets higher for each pixel).
is there a way to force the model to stay on 0 (y axis) but still let it grow as each point gets different number of iterations?
i’ve tried to find the point which requires the smallest amount of iterations(and basically the lowest point in the set) and subtracts it from all points but that didn’t work.(since num of iterations changes every zoom process it made the set jump from value 5 to 100 for example).
This problem happens to 2D fractal maps as well, the escape value’s color representation “shifts”. If you zoom with a factor of 10, every 10th point should be a point from a non-zoomed version, but as iterations grow along with zoom these points will not be the same.
The solution (for me it was) is to find the largest zoom which you want to achieve, find the appropriate iteration factor for that zoom level (for precise calculations), and apply this iteration factor every time even for zoom level 0.
This will make the calculation slow, in my case I had to iterate every point 5000 times regardless of zoom level.