Images of fractals can be created by fractal generating programs.

1) Iterated function systems – use fixed geometric replacement rules; may be stochastic or deterministic;[32] e.g., Koch snowflake, Cantor set, Haferman carpet[33], Sierpinski carpet, Sierpinski gasket, Peano curve, Harter-Heighway dragon curve, T-Square, Menger sponge

2) Strange attractors – use iterations of a map or solutions of a system of initial-value differential equations that exhibit chaos (e.g., see multifractal image)

3) L-systems - use string rewriting; may resemble branching patterns, such as in plants, biological cells (e.g., neurons and immune system cells[17]), blood vessels, pulmonary structure,[34] etc. (e.g., see Figure 5) or turtle graphics patterns such as space-filling curves and tilings

4) Escape-time fractals – use a formula or recurrence relation at each point in a space (such as the complex plane); usually quasi-self-similar; also known as "orbit" fractals; e.g., the Mandelbrot set, Julia set, Burning Ship fractal, Nova fractal and Lyapunov fractal. The 2d vector fields that are generated by one or two iterations of escape-time formulae also give rise to a fractal form when points (or pixel data) are passed through this field repeatedly.

5) Random fractals – use stochastic rules; e.g., Lévy flight, percolation clusters, self avoiding walks, fractal landscapes, trajectories of Brownian motion and the Brownian tree (i.e., dendritic fractals generated by modeling diffusion-limited aggregation or reaction-limited aggregation clusters).[6]