Stumbling across the Gumowski-Mira equation in 1992, I quickly created a simple program (on an A3000) to explore the equation. From 1992 until 2006, I had found few examples of Gumowski-Mira fractals / attractors ('Mira fractals') either on the Internet or within fractal applications. Despite Mira fractals not possessing the complexity or visual impact of some other types of fractals, they can still be beautiful in their own way – sometimes creating patterns with striking similarities to forms present in the natural world (such as single-celled organisms, feathers, and citrus fruit halves). The general neglect of this intriguing fractal variant seems seemed a pity. (Since 2007, generative programmer-artists such as Keith Peters and Tom Beddard have done much to raise the awareness of Mira fractals.)
The Gumowski-Mira equation is:
The equation was developed at the CERN research centre in 1980 by I. Gumowski and C. Mira – not to create fractals, but to calculate the trajectories of sub-atomic particles.
Images from the Mira Fractal generator:
» download Mira 1.2 (Win 2k/XP/Vista/7; 64kB ZIP) – non-GUI version, adjustable parameters (coded for fast rendering – not usability)
» download Mira 1.2 (Linux; 55kB ZIP)
» download Mira 2.0 (Win 98/2k/XP; 11kB ZIP) – GUI version (resizable, small, easy-to-use, slow)
The freeware applications contained in the ZIP files on this page are standalone executables (McAfee report). Please note the OS version compatibility list beside each Windows application.
Some screensavers fail to initiate on my Windows PCs while the Mira 1.2 executable is running / minimised. As yet, no issues have been reported to me. Nevertheless, I have to state a disclaimer: this software is supplied as is, and the author accepts no liability for damages, direct or consequential, which may result from the use of this software.
One of the main advantages of compiled executables is fast screen rendering. However, if you wish to avoid executables, there are alternatives in the other generators below.
Other Mira Fractal Generators
Art From Code Miras by Keith Peters
Gumowski-Mira Patterns by subblue
Mira Paint by MSL (Flash AS3 below; left mouse click for new colour, <space> to clear)
Hopalong – Barry Martin fractals
» download Tiny Hopalong (Win 98/2k/XP; 5kB ZIP)
» download Screensaver (Win 2k/XP/Vista/7; 57kB ZIP)
Psych Weave Pattern
» download Screensaver (Win 2k/XP/Vista/7; 60kB ZIP)
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