Fractal Friday 2020.02.21

I started this week's Fractal Friday exploration by trying out higher-iteration-cutoff Mandelbrot sets.  Here are a few results with max iterations set to 1000, and higher breakout values than my usual setting of 10.0 - more detail definitely appears, especially in the boundary of the breakout value which becomes much more frond-like. The first one also includes a geometric texture backdrop layered in with MathPaint.





 I also tried the same with Julia sets, but at least for the parameters I was exploring had less luck there because Julia set thresholds seem to be a bit more abrupt. If values escape after 100 iterations, it's not easy to find higher breakout values that will permit higher iterative attempts to reveal more detail around the breakout boundary in the same way as Mandelbrot. Nonetheless I found some cool results, including this spiral that again has a MathPaint geometry-layer background:





I'm including a couple of different takes on the last one. First there's the base Julia Set image with some nice spiral figures. The image that follows uses the same parameters, xy-range and color mapping, but with a real-valued warp function added. The 'warp' is an inverse exponential function applied to the real part of z for each calculation, and the results are pretty cool. I include a couple of extra zooms into this warped fractal below.









I'm going to post some updates on the geometry renderer of MathPaint in the coming days - check back on the blog or follow on Facebook, Twitter, Instagram, or Pinterest!