For a standard 2D or 3D Mandelbox, the radius of the sphere of inversion (InvRadius) and the maximum distance a point can be from the inversion origin in order for the conditional inversion to be applied (MaxRadius) are equivalent. I've been experimenting with separating these, so in pseudocode the conditional inversion becomes:
if (point.length < MinRadius)
point *= constant
else if (point.length < MaxRadius)
point *= InvRadius^2 / point.length^2
Here's a few images where the only parameter being changed is MaxRadius relative to constant InvRadius. For param visualization:
InvRadius ==> yellow
MaxRadius ==> green
MinRadus ==> red
MaxRadius = InvRadius
MaxRadius < InvRadius
MaxRadius > InvRadius
For MaxRadius < InvRadius this results in a ring region between MaxRadius and InvRadius circles where points under iteration do not get inverted (compared to MaxRadius = InvRadius)
For MaxRadius > InvRadius this results in a ring region between MaxRadius and InvRadius where points under iteration get inverted
inward (rather than
outward as in standard Mandelbox conditional sphere inversion)
Has this been tried before? I looked through a number of Mandelbox/AmazingBox formulas and didn't find anything similar, but with so many different variants in different programs I could have easily missed a pre-existing version of this.
I've tried this idea for the 3D Mandelbox as well, but results are murky. I think in 3D this causes what are referred to as cuts? Or tears? Which makes sense in terms of discontinuities in the conditional inversion when MaxRadius != InvRadius. Thinking I should try an AmazingSurface version next.
Fragmentarium frag files for 2D version are atttached, and include three-way param visualization overlay.
August 02, 2010, 05:20:18 AM
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