The Mathaesthetics software has made some cool advances this week, and we’re celebrating with our first Fractal Friday video!
These images depict a Julia set of degree 3 (function z^3 + C), with the C value 0.4+0.7i, 50 iterations maximum, and the escape value slowly changing with each image. The first image has escape value 0.8:
Midway we spend a lot of time in the “merge” around the breakout value 1.08:
This ultimately stabilizes in the frilly pinwheels that we see at breakout value 1.5:
In these images, we use three different colors to map between. At the low-iteration end is a deep sapphire (RGB 0.0, 0.4, 0.7), a little past halfway (iteration 33) is mapped to an electric blue (RGB 0.5, 0.8, 1.0), and from there we pivot toward the final color at iteration 48 and above, a canary yellow (RGB 1.0, 1.0, 0.4). This is a multi-color-gradient mapping, and the software now supports any arbitrary number of gradient stops along the iteration scale, which permit both better detail exposure and greater aesthetic possibilities than just mapping the start and end colors.
There’s a more subtle difference to this image as well: the graded colors in between can now be calculated different ways. The software now has options for logarithmic and exponential curves (which bias one side or the other of the color gradient), parabolic curves (which tend to highlight both ends and show fewer blended colors), and normalized gradient calculation, which favors blended colors (the choice for these images). In the normalized gradients the visual effect tends to be gentler between two colors with more visibility of gradations – this is evident in the sapphire-to-electric-blue curves which are less visible with a linear color mapping.
These differences in color mapping algorithm are more evident when there are more iteration levels in a fractal image. For contrast, here’s a rendering of the same final image with regular linear gradient and just two colors specified (sapphire to canary yellow):
There’s a little more info on the different modes of color mapping in yesterday’s post on our new noise renderer.