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
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
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 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
This week’s images are mostly from the same region, x-axis: (-1.308, 0.567), y-axis (-0.542, 1.351). I started with the Douady rabbit – setting C to -0.123 + 0.745i, with max iterations for these renderings set to 32 and the escape radius set to 1000.0. Each of the following is produced by an adjustment to C … Read moreFractal Friday! 2019.11.22
My new vector field renderer prototype is chugging along, and combined with hooking up .png output to the app I was able to make a couple of little animations with it. The vector function is a combination of trig and exponentiation (mixing up x and y to keep things interesting across the plane). These animated … Read moreStrawberry vector fields forever
This week I’m beginning a new series of postings, to celebrate the implementation of a fractal renderer in our flagship product – Fractal Friday! Click on each image to see it full size. These are window captures at screen resolution; our final product will also support higher resolutions and larger sizes. This first collection was … Read moreFractal Friday! 2019.11.15