ICYMI, I’m currently writing an application that generates mathematical art. It’s created in Swift, for Mac OS desktop systems. All the images on this blog are created from it, including the fractals posted every Fractal Friday.
This week I hooked up a full range of CoreImage effects to the app, and I’m having fun sending fractals through tiling effects to create some really cool repeating patterns.
For the first one I used a small 320×320 source image of an edge-rendered Julia set section
I played around with this image using the Twelvefold Reflected Tile and Eightfold Reflected Tile filters to get these:
I used a more psychedlic-looking color-banded Mandelbrot section for the next set:
The tiled patterns produced vary depending on the angle and width of the tiling as well as the filter chosen:
This grayscale gradient Julia set creates some nice patterns:
Here’s another edge-drawn fractal using an altered Julia set using z^5 instead of z^2, and two tiled patterns made from it:
Finally, this color-gradient-rendered Julia set image was used to generate two results, and the third pattern is actually just a combination of them – the filter chain in the application lets you apply as many filters as you like, save them with custom settings, and turn them on and off to see different combinations.
More to come next week, plus screenshots and teasers as the flaship Mathaesthetics application gets closer to beta release! You can follow Mathaesthetics on Facebook, Twitter, Instagram, and Pinterest.