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
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
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
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
It’s Fractal Friday! As always you can click the images below to see them full-size. This week’s fractal images highlight two new features added to the application I’m developing: color cycles, and Nth-degree fractal expressions. A color cycle is an an array of colors used to render the fractal pixels. The renderer cycles through them … Read moreFractal Friday! 2019.11.29