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
It’s Friday already! This week I’ve been jamming on this application UI development, including a brand-new feature to support fractals: the color mapping control: For fractal rendering the integers below each color correspond to the output value (escape iterations) to which the color is assigned. The linear-gradient mapping mode means that colors between these values … Read moreFractal Friday 2019.12.13
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
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 … Read moreFractal Friday 2019.12.06
It’s day one of noise generation in our flagship product! There are many ways to generate visual noise; our first algorithm is a simple static pixel generator. For these examples I’m generating a random integer from 0 to 255 and using that value to calculate a color on the gradient between two colors (here, blue … Read moreFlavors of static: random distributions and noise
I’m spending a lot of time in Cocoa drawing and Core Graphics lately, working in Swift. The API around the Core Graphics CGPattern object in Swift is a little challenging – it requires C callbacks and unsafe pointers for basic pattern-creation and drawing functionality. It also doesn’t work exactly as I’d like it to; I … Read moreDev notebook: brush-like drawing in Swift, without CGPattern