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
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’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
If you’ve been following Mathaesthetics posts you’ve seen a variety of images shared – different types of generated art from fractals to repeated 2D plots to vector fields and scalar fields and more. All images on this blog are created by our flagship software product, which has been in development since November 2019. Today for … Read moreHello World, from MathPaint! (Preview)
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
I worked on my first GameplayKit project earlier this year and there were things I liked about the lightweight, general state-machine model provided by the GKState and GKStateMachine classes. However I also found a few odd patterns in these classes: their implementation without using enumeration values for states, the inelegant (StateClass).class.self syntax model required by … Read moreDev notebook: an enum alternative to GKState / GKStateMachine
The fractal renderer used to draw this week’s graphics has a new feature – rendering in ‘edge’ mode. Rather than filling the value regions with different colors, edge-mode detects the change in output values and draws a line at the boundary between them. Here’s the classic Mandelbrot set rendered this way: Here’s a simple black-and-white … Read moreFractal Friday 2019.12.20
The Mathaesthetics flagship app will support a number of modes of mathematical image creation. I spent most of yesterday working on and improving the scalar field renderer. In a scalar field, a function f(x, y) produces a value for each point. This scalar value is then mapped to a color gradient. I’m exploring both different … Read moreScalar fields for gradients and other graphic patterns
The standard Cocoa control NSSlider comes in a circular variety that resembles a rotating knob with an indicator point. Among the ideal applications for such a control is representing a circular angle. In the application I’m developing I wanted to use this to control the angle of the brush image used for drawing. I began … Read moreDev notebook: Converting scale & position of circular NSSlider for degrees
I’m excited to share today’s image generated from the application under development: It’s a pretty organic background-pattern sort of texture, but it highlights a few cool things about the app, which is focused on creating beautiful images with mathematical techniques. First, the brush strokes! All of these strokes are ‘points’ drawn with an extra-wide calligraphy … Read morePainting with Trigonometry