For today’s post I’m showing off some the Apple Core Image effects capabilities built into MathPaint, with three Julia set fractals. By the way, MathPaint’s release is now close enough for crowdfunding – please see our MathPaint IndieGoGo campaign for details, and a video of the application in action! For each Julia set in this … Read moreFractal Friday 2020.02.28
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 … Read moreFractal Friday 2020.02.21
Here are some extended Julia Set (z^7) floral fractals for Fractal Friday, Valentine’s Day edition – share them with your sweetheart! This week’s images are all zooms of the same set (unchanged function parameters and color mappings). All images made with MathPaint, the flagship application for generative graphics on Mac OS X currently in development … Read moreFractal Friday 2020.02.14
This week I’m sharing the results of a cool new feature in MathPaint: fractals warped by real-valued functions. The application now supports defining a custom real-valued function that is applied during each iterative evaluation to the real part of the complex number ‘z’, before z is squared. The possible effects are endless – from slight … Read moreFractal Friday 2020.02.07
For this week’s post I’m showing off more of the rendering and layer-compositing options that are part of MathPaint. I’m using the same fractal settings for all of this week’s images – a Mandelbrot set with breakout value at 10.0, max iterations set to 200, and viewed at the (approximate) ranges [-1.432, -1.345] on the … Read moreFractal Friday 2020.01.31
This week I’ve been busy working on the MathPaint architecture so didn’t develop any obvious fractal rendering features… Though I did succeed in getting some optimizations in to speed things up, and the fractal renderer is now fully concurrent (using Cocoa OperationQueue and Operation objects.) This week I chose to explore another of my favorite … Read moreFractal Friday 2020.01.24
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 … Read moreFractal Friday 2020.01.17
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 … Read moreFractal Friday 2020.01.10
The noise renderer has gotten more sophisticated in the past week, and it’s being put to work in this week’s set of fractals. Each image includes a generated noise-texture, with various approaches to transparency in the fractal permitting the texture to show through. The Julia set image above has a semi-transparent purple in the color … Read moreFractal Friday 2020.01.03
It’s the last Fractal Friday of the year, time for some recursive magic! This week we’re exploring the Mandelbrot set, using two features of the Mathaesthetics prototype software: deep color mapping, and a new helpful zoom feature. Here’s where we start: In this image, there’s a color mapping with 10 different colors at various levels … Read moreFractal Friday 2019.12.27