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 skewing to complete warping of the image, but generally the fractal retains its self-similarity and zoomability, as long as the real function doesn’t drive it to a premature divergence or convergence.
A variety of approaches produced the images below, including use of a sine function with different powers of the input argument, a step function (a simple round() with some scaling applied), and a natural-log-base exponential function. All are warped Julia sets except for the next-to-last, which is based on Mandelbrot. A variety of MathPaint graphics features are also used such as edge drawing and different forms of color mapping.
