Sprott's Fractal Gallery

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Fractal of the Day

[FRACTAL OF THE
                    DAY]

Every day at a few minutes past midnight (local Wisconsin time), a new fractal is automatically posted using a variation of the program included with the book Strange Attractors: Creating Patterns in Chaos by Julien C. Sprott. The figure above is today's fractal. Click on it or on any of the cases below to see them at higher (640 x 480) resolution with a code that identifies them according to a scheme described in the book. Older Fractals of the Day are saved in an archive. If your browser supports Java, you might enjoy the applet that creates a new fractal image every five seconds or so. If you would like to place the Fractal of the Day on your Web page, you may do so provided you mention that it is from Sprott's Fractal Gallery and provide a link back to this page. If you want to make your own fractals, I recommend the Chaoscope freeware.


Chaos Demonstrations

[juliaset]

The following rather standard fractals are low-resolution sample screen captures from the Chaos Demonstrations program by J. C. Sprott and G. Rowlands. You may also want to view an index of these and many other screen captures from the program.


Strange Attractors

[plate03]

The following fractals are low-resolution sample color plates from the book Strange Attractors: Creating Patterns in Chaos by Julien C. Sprott. You may also want to view an index of all 371 figures from the book.


More Strange Attractors

[inrrxlce]

The following 3-dimensional strange attractors are mostly from the book Strange Attractors: Creating Patterns in Chaos by Julien C. Sprott but are here rendered in higher (800 x 600) resolution with the third dimension mapped to a palette of 256 colors. Additional such cases can be produced automatically by the program sa256.exe that searches for chaotic solutions of a general system of quadratic maps with 30 coefficients.


Julia Sets

[af206d1a]

The following fractals are standard Julia sets of the function z^2 + c. They were produced automatically by the program julia256.exe by J. C. Sprott that searches the complex-c plane for interesting cases. The names consist of two four-digit hexadecimal numbers p and q such that c is given by c = -2 + p / 21845 + i q / 43691. The plots cover the range z = (-0.02, 0.02) + (-0.02, 0.02) i.


Quadratic Map Basins

[eparxhhp]

The following fractals are generalized Julia sets of 2-D quadratic maps with twelve coefficients. They were produced automatically by the program genjulia.exe by J. C. Sprott that searches the 12-dimensional space of coefficients for interesting cases. The technique is described in a paper "Automatic Generation of General Quadratic Map Basins" by J. C. Sprott and C. A. Pickover. The coefficients are coded into the names according to a scheme described in the book Strange Attractors: Creating Patterns in Chaos. The plots cover the range -1 < x < 1 and -1 < y < 1. A few additional images of this type produced with the program Fractal eXtreme by Cygnus Software are available.


Iterated Function Systems

[arigiedm]

The following fractals are iterated function systems generated by the random iteration algorithm using two linear affine transformations. Color is introduced according to the number of successive applications of each transform. They were produced automatically by the program ifs256.exe by J. C. Sprott that searches the 12-dimensional space of coefficients for interesting cases. The coefficients are coded into the names according to a scheme described in the paper "Automatic Generation of Iterated Function Systems".


Strange Attractor Symmetric Icons

[ofnacawl]

The following icons are produced from 3-D strange attractors by mapping the x-coordinate to radius and the y-coordinate to angle and replicating the pattern with different orientations. The z-coordinate is represented by one of 256 colors, and a shadow is added to enhance the illusion of depth. The technique is described in a paper "Strange Attractor Symmetric Icons" by J. C. Sprott. The equations used are coded into the name according to a scheme described in the book Strange Attractors: Creating Patterns in Chaos by Julien C. Sprott. Additional such cases can be produced automatically by the program icon256.exe. If you like these, you can view an index of 100 additional such examples, or an index of cyclic symmetric attractor anaglyphs produced by a different method. You can also view an index of fractal tilings useful as Windows wallpaper or HTML backgrounds (as on this page).


Newsgroup Collection

[medusa]
Image courtesy of Paul Carlson

You might also like to look at an index of many thousands of fractals I've collected off the net, mostly from the newsgroup alt.binaries.pictures.fractals and from the World Wide Web. In most cases, I don't know the original source, and so I apologize to anyone whose copyright may have been violated. Many of the nicest of these images are the work of Paul Carlson whose Fractal Gallery you may wish to visit. Here's a few cases I've selected as the best of the best:


Animated GIF Attractors

[Animated GIF]

These images are from the iterated mapping xnew = a + bx + cx2 + dy + ez + f sin(pi t/8), ynew = x, znew = y, where a through f are constants coded into the file name as described above. If your browser supports animated GIFs, you will see 16 looping frames (t mod 16). These images illustrate the stretching that causes chaos and the folding that produces the fractal microstructure of strange attractors. The DOS programs that were used to produce them are available. The individual frames were assembled using the GIF Construction Set by Alchemy Mindworks Inc. You might also like to look at an index of other fractal GIF animations, which includes 19 of the simplest known chaotic flows.


Natural Fractals

[Broccoli]

These images are real-world fractals photographed by J. C. Sprott. More images of this type can be found in the index of natural fractals.


Publication Quality Attractors

[Publication quality
                  attractor]

These very high resolution (4400 x 3200) strange attractors (c) by J. C. Sprott are included for anyone who would like to make publication quality prints or display art. You may publish or display them without further permission provided you acknowledge their source. Thousands more like these are available upon request. See also the slideshow and high-resolution images from the CD-ROM that accompanies the book "Images of a Complex World: The Art and Poetry of Chaos" and the strange attractor prints offered for sale.


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