Chaotic
Attractors
February
27, 1998
The original IMA attractor was computed in 1989 on an
Apollo DN 10000 in Sydney, Australia. Subsequently, in 1994,
the image was recomputed on an SGI Indigo at the University
of Houston. The latest version of the Logo was computed in 1998
on a Linux PC by Mike Field
of the University of Houston. The base image was computed at
8000 lines of resolution.
Symmetric attractors of this type ("Symmetric
Icons") are computed by iterating a polynomial map with
dihedral or cyclic group symmetry. The IMA attractor has the
symmetry of an equilateral triangle. The attractor was computed
by taking 6 billion iterations of the complex polynomial map
 ,
with initial point  .
(In fact only half the image was computed - the other half was
obtained using the reflectional symmetry of the attractor.)
The coloring and shading of the image is related to the number
of times each pixel is visited in the iteration and reflects
the statistics of the iteration. Both the iteration and coloring
program are part of the software package prism (PRogram
for the Interactive Study of Maps, © Michael Field, 1996).
As well as the complete image, we give a number of images showing
detailed magnifications of various pieces of the logo.
More
information about symmetric attractors (and many more pictures)
can be found in the book Symmetry
in Chaos by Michael
Field and Martin Golubitsky,
published in 1992 by Oxford University Press. See also the article
Symmetric chaos: how and why, Notices AMS 42 No.
2 (1995), 240-244.
Mike
Field & Marty Golubitsky
(University of Houston, February 1998)
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