This week’s images again come from some experiments with new features for MathPaint, the flagship software app I’m working on.
Previously I posted some experiments with edge rendering in fractal geometry, where only the boundary between levels of output are drawn. It shows the boundary between iteration levels but does not indicate the level itself (which is normally shown by a color gradient value).
This week’s experiment takes a different approach to interpreting iteration values, which are integers in a fairly small range (usually 1 to 100 or at most a few hundred). Rather than render the level as a color, we convert it to a size – and draw a shape centered at the point, at the indicated size. Higher iterations create bigger shapes, quick iteration boundaries create very small shapes. We use a sparser grid (only evaluating one of ever five, eight, or 10 pixels – the setting can be adjusted). The idea is similar to an alternate vector field rendering which was explored in this blog.
Here’s the familiar Mandelbrot set, rendered with squares drawn at sizes corresponding to iteration levels:
I like the rather stark, structured aesthetic that the squares lend to the shape. A bit more lively is this Julia set zoom, drawn with the same square shapes (and a different line color):
Different shapes can change the character of the rendered images. Here’s a z^5 julia set (one of my favorite forms) rendered with circles, drawn with a 2-point line:
And a zoom in on the same image, with background and foreground colors changed – I like this as an abstract image that isn’t recognizably a fractal, but the underlying math gives subtle organic pattern to parts of it:
Finally here is a regular Julia set rendered with 45° diagonal lines, first zoomed in, then zoomed back out with thinner lines:
More MathPaint screenshots and mathematical art coming next week! You can follow Mathaesthetics on Facebook, Twitter, Instagram, and Pinterest.