Fractal-generating software is any type of graphics software that generates images of fractals. There are many fractal generating programs available, both free and commercial. Mobile apps are available to play or tinker with fractals. Some programmers create fractal software for themselves because of the novelty and because of the challenge in understanding the related mathematics. The generation of fractals has led to some very large problems for pure mathematics.

Fractal generating software creates mathematical beauty through visualization. Modern computers may take seconds or minutes to complete a single high resolution fractal image. Images are generated for both simulation (modeling) and random fractals for art. Fractal generation used for modeling is part of realism in computer graphics. Fractal generation software can be used to mimic natural landscapes with fractal landscapes and scenery generation programs. Fractal imagery can be used to introduce irregularity to an otherwise sterile computer generated environment.

Fractals are generated in music visualization software, screensavers and wallpaper generators. This software presents the user with a more limited range of settings and features, sometimes relying a series pre-programmed variables. Because complex images can be generated from simple formula fractals are often used among the demoscene. The generation of fractals such as the Mandelbrot set is time-consuming and requires many computations, so it is often used in benchmarking devices.

The generation of fractals by calculation without computer assistance was undertaken by German mathematician Georg Cantor in 1883 to create the Cantor set. Throughout the following years, mathematicians have postulated the existence of numerous fractals. Some were conceived before the naming of fractals in 1975, for example, the Pythagoras tree by Dutch mathematics teacher Albert E. Bosman in 1942.

The development of the first fractal generating software originated in Benoit Mandelbrot's pursuit of a generalized function for a class of shapes known as Julia sets. In 1979, Mandelbrot discovered that one image of the complex plane could be created by iteration. He and programmers working at IBM generated the first rudimentary fractal printouts. This marked the first instance of the generation of fractals by non-linear creations laws or 'escape time fractal'. Loren Carpenter created a two-minute color film called Vol Libre for presentation at SIGGRAPH in 1980. The October 1983 issue of Acorn User magazine carried a BBC BASIC listing for generating fractal shapes by Susan Stepney, now Professor of Computer Science at the University of York. She followed this up in the March 1984 Acorn User with “Snowflakes and other fractal monsters”. Fractals were rendered in computer games as early as 1984 with the creation of Rescue on Fractalus!. From the early 1980s to about 1995 hundreds of different fractal types were formulated.

The generation of fractal images grew in popularity as the distribution of computers with a maths co-processor or floating-point unit in the central processing unit were adopted throughout the 1990s. At this time the rendering of high resolution VGA standard images could take many hours.^{[citation needed]} Fractal generation algorithms display extreme parallelizability. Fractal-generating software was rewritten to make use of multi-threaded processing. Subsequently, the adoption of graphics processing units in computers has greatly increased the speed of rendering and allowed for real-time changes to parameters that were previously impossible due to render delay. 3D fractal generation emerged around 2009. An early list of fractal-generating software was compiled for the book titled Fractals: The Patterns of Chaos by John Briggs published in 1992. Leading writers in the field include Dietmar Saupe, Heinz-Otto Peitgen and Clifford A. Pickover.

There are two major methods of two dimensional fractal generation. One is to apply an iterative process to simple equations by generative recursion. Dynamical systems produce a series of values. In fractal software values for a set of points on the complex plane are calculated and then rendered as pixels. This computer-based generation of fractal objects is an endless process. In theory, images can be calculated infinitely but in practice are approximated to a certain level of detail. Mandelbrot used quadratic formulas described by the French mathematician Gaston Julia. The maximum fractal dimension that can be produced varies according to type and is sometimes limited according to the method implemented. There are numerous coloring methods that can be applied. One of earliest was the escape time algorithm. Colour banding may appear in images depending on the method of coloring used as well as gradient color density.

Some programs generate geometric self-similar or deterministic fractals such as the Koch curve. These programs use an initiator followed by a generator that is repeated in a pattern. These simple fractals originate from a technique first proposed in 1904 by Koch.