Fractal-generating software
Fractal-generating software is any type of
Fractal generating software creates
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.[4] The generation of fractals such as the Mandelbrot set is time-consuming and requires many computations, so it is often used in benchmarking devices.[5]
History
The generation of fractals by calculation without computer assistance was undertaken by German mathematician Georg Cantor in 1883 to create the Cantor set.[6] 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.[7] This marked the first instance of the generation of fractals by non-linear creations laws or 'escape time fractal'.[8][9] Loren Carpenter created a two-minute color film called Vol Libre for presentation at SIGGRAPH in 1980.[10] 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.[11][12] She followed this up in the March 1984 Acorn User with “Snowflakes and other fractal monsters”.[13] 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.[14]
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.[15] 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.[16] Leading writers in the field include Dietmar Saupe, Heinz-Otto Peitgen and Clifford A. Pickover.
Methods
There are two major methods of two dimensional fractal generation. One is to apply an iterative process to simple equations by generative recursion.[6] 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.[17] Mandelbrot used quadratic formulas described by the French mathematician Gaston Julia.[14] 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.[14] Colour banding may appear in images depending on the method of coloring used as well as gradient color density.
Some programs generate
The other main method is with
Three dimensional fractals are generated in a variety of ways including by using
Features
Many different features are included in fractal-generating software packages. A corresponding diversity in the images produced is therefore possible. Most feature some form of
One feature of most escape time fractal programs or algebraic-based fractals is a maximum iteration setting. Increasing the iteration count is required if the image is magnified so that fine
External media | |
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Images | |
Cover of Scientific American, August 1985 | |
Video | |
Vol Libre 1980 by Loren Carpenter | |
Realtime escape-time fractal rendering with a GPU | |
Four-dimensional raytraced animation in POV-Ray |
Standard graphics software (such as
Programs
Because of the
There are many fractal generating programs available, both free and commercial. Notable fractal generating programs include:
- Apophysis – open source IFS software for Microsoft Windows-based systems
- Bryce – cross platform commercial software partially developed by Ken Musgrave
- Mac OS. Free for non-commercial use.
- Electric Sheep – open source distributed screensaver software, developed by Scott Draves.
- Fractint – MS-DOS freeware initially released in 1988 with available source code, later ported to Linux and Windows (as WinFract)
- Fyre is a cross-platform open source tool for producing images based on histograms of iterated chaotic functions
- Kalles Fraktaler – Windows based fractal zoomer
- Milkdrop – music visualization plugin distributed with Winamp
- MojoWorld Generator – a defunct landscape generator for Windows
- openPlaG – creates fractals by plotting simple functions
- Picogen - a cross platform open source terrain generator
- Sterling – freeware software for Windows
- fractal terraingenerator that can render animations for Windows and Mac OS X
- Ultra Fractal – proprietary fractal generator for Windows and Mac OS X
- Wolfram Mathematica – can be used specifically to create fractal images
- XaoS – cross platform open source fractal zooming program
Most of the above programs make two-dimensional fractals, with a few creating three-dimensional fractal objects, such as mandelbulbs and mandelboxes. Mandelbulber is an experimental, cross platform open-source program that generates three-dimensional fractal images.[27] Mandelbulber is adept at producing 3D animations.[28] Mandelbulb 3D is free software for creating 3D images featuring many effects found in 3D rendering environments.[29] Incendia is a 3D fractal program that uses Iterated Function Systems (IFS) for fractal generation.[30] Visions of Chaos, Boxplorer and Fragmentarium also render 3D images.
The open source GnoFract 4D is available.[31] ChaosPro is freeware fractal creation program.[32] Fraqtive is an open source cross platform fractal generator.[33] MandelX is a free program for rendering fractal images on Windows.[34] WinCIG, Chaoscope, Tierazon, Fractal Forge and Malsys also generate fractal images.
See also
References
- ISBN 978-0300197877. Retrieved 5 May 2017.
- ISBN 9783642956782. Retrieved 7 May 2017.
- ^ .
- ^ Janus Kopfstein (14 May 2014). "This 4-kilobyte demo squeezes a universe of fractals into the size of a Word document". The Verge. Vox Media. Retrieved 5 March 2017.
- ISBN 9783642399589. Retrieved 7 May 2017.
- ^ a b Daniel Shiffman. "Chapter 8. Fractals". The Nature of Code. Retrieved 22 Jan 2024.
- ISBN 978-0143113454.
- ^ Tom Van Cutsem. "Session 5 - Escape-Time Fractals". Retrieved 7 March 2017.
- ISBN 9783110250077. Retrieved 7 May 2017.
- ^ "Vol Libre: The First Fractal CGI Movie". History of Information. Jeremy Norman & Co. Retrieved 5 March 2017.
- ^ "Susan Stepney Professor of Computer Science, University of York, UK". www-users.cs.york.ac.uk. University of York. Retrieved 29 December 2018.
- ^ Stepney, Susan (October 1983). "Incredible fractals, pp 37, 39, 41 and 43". www-users.cs.york.ac.uk. AcornUser. Retrieved 29 December 2018.
- ^ Stepney, Susan (March 1984). "Snowflakes and other monsters, pp 25, 28, 29". www-users.cs.york.ac.uk. AcornUser. Retrieved 29 December 2018.
- ^ CiteSeerX 10.1.1.393.9370.
- arXiv:1611.03079 [cs.GR].
- ISBN 978-0671742171.
- ISBN 9789814603744. Retrieved 5 May 2017.
- ISBN 978-1489925787. Retrieved 5 May 2017.
- .
- ISBN 978-0883859711. Retrieved 7 May 2017.
- .
- ^ "Turtle Graphics Renderer". Retrieved 2 March 2017.
- ^ "Fractal Lab". subblue.com. Retrieved 5 March 2017.
- ^ "Welcome to the official home of the JWildfire software!". Retrieved 7 March 2017.
- ^ Mike Williams (17 July 2016). "Mandelbrot Fractal". PCAdvisor. IDG UK. Retrieved 5 March 2017.
- ^ "Fractal Grower". The University of New Mexico. Retrieved 6 March 2017.
- ^ Joey Bernard (7 January 2014). "Taking Fractals off the Page". Linux Journal. Retrieved 5 May 2017.
- ^ Mike Williams (25 November 2013). "Generate spectacular 3D fractals with Mandelbulber". BetaNews. Retrieved 5 March 2017.
- ^ "Mandelbulb 3D (MB3D) Fractal Rendering Software". SphereLab. 17 January 2014. Retrieved 7 March 2017.
- ^ "Incendia". Ramiro Pérez Clare Nash. Retrieved 7 March 2017.
- ^ "Gnofract 4D". Retrieved 2 March 2017.
- ^ "ChaosPro Release 4.0". Retrieved 2 March 2017.
- ^ "Fraqtive". Retrieved 2 March 2017.
- ^ "Free software from Falcosoft". Falcosoft. 27 January 2017. Retrieved 5 March 2017.
External links
- Fractal-generating software at Curlie
- An Introduction to Fractals by Paul Bourke, May 1991