Hello all. Very interesting progress so far.
Twinbee... any chance of you extending your article so it has a page 3 titled "for coders" or something similar? ie, a pseudo code structure for someone wanting to try these formulas out who is more programming inclined rather than mathematically inclined.
Assuming that the reader has a basic raytracer or raymarcher coded up and have the ability to have a ray starting from the "camera" and know the "direction" the ray is going, then you step a certain amount along the ray and repeatedly try the mandelbulb formula to see if the point is inside or outside the set and plot the point in 3D space accordingly.
The basic code would be along the lines of
for y=1 to bitmapheight do
for x=1 to bitmapwidth do
<calculate vector of ray direction from camera to pixel location in 3d space>
<now we have the starting point in XYZ coords (this would be the bitmap XY coordinate converted to XYZ space in 3d)>
<feed the point XYZ into distance estimator>
<test point returned from distance estimator by iterating it through the iteration loops>
if ((x^2+y^2+z^2)>4) or (iterations>256) then giveup else XYZ is a valid point so raytrace the point
1. The z triplet and c triplet both have 3 xyz parameters
2. So Z starts as (1,0,0) and C starts as (X,Y,Z) when iterating the formula?
3. Does the distance estimator calc happen while the iteration happens?
4. Am I on the right track?
It would also be nice to have a series of "DistanceEstimatorNylander" "IterateNylander", "DistanceEstimatorMakin" "IterateMakin" snippets of code depending on who first came up with the idea. Looking back over this thread shows many attempts that may not be the true 3d mandelbrot type, but never the less result in interesting results. It would be great to have some info along the lines of "the above picture uses the following formula by whoever" and have the relevant snippet/change in code for distance estimation and iteration.
Or even a basic sample code for distance estimation and iteration of the now classic ^8 result. Enough to get the basic framework going and have a play with these sort of images.
Keep going regardless guys. There is some great results in this thread so far.