C/C++

Okay, so the bifurcated Mandelbrot set is a "made up" term, but the name reflects its elegant demonstration of the relationship between the logistic map bifurcation diagram and the Mandelbrot set. The connection between these two facets of chaos theory is often overlooked but a little math goes a long way to clarify the matter. For its combined elegance and complexity, not to mention its simple beauty, it is my all-time favorite render.

Ray Marching is a 3D rendering technique similar to Ray casting. Unlike ray casting, which use an intersection function, ray marching uses a distance estimation function to march rays forward. For objects with well-defined distance estimation functions, in particular fractals, this can be an excellent way to produce detailed renders.

Chaotic attractors are equations iteratively applied to vectors, such that the path traced by the vector produces a fractal structure. The Lorenz Butterfly is the most well-known example, but many such attractors exist. They can be visualized by applying the attractor iteratively to many points and then rendering them out.

The Buddhabrot is a technique for plotting the Mandelbrot set that produces particularly unique and beautiful imagery.

Cubic Spline Interpolation is a shockingly complex but very effective technique for producing a twice-differentiable function that passes through a set of given points.

The Utility library contains a variety of tools I've built for various purposes. They contain classes for vectors from 1 to 4 dimensions, an implementation of quaternions used for rotation, functions for generating Worley and simplex noise, collision detection functions, and more.

Newton's fractal is a fractal created by iterating Newton's equation many times over a variety of points, and then coloring those points based on where the iterative sequence ended up. It can produce some interesting images as well as videos.