Chaotic attractors with planar symmetry
These images appeared at the APL97 conference in Toronto in August 1997.
The images were created by Nathan Carter, Richard Eagles, Stephen Grimes,
Andrew Hahn, and Clifford Reiter and the exhibit was titled
"Chaos with Symmetry". The work
resulted from a National Science Foundation
Research Experience for Undergraduates program
at Lafayette College, Easton, PA, USA during the summer of 1997.
The images were created with J which is a dialect of APL . The images here contain 10-20 times fewer
pixels than the original files used to create the prints described. While
web pointers to this work are welcome, the authors expect other use to
be with acknowledgement and permission.
The mathematics used in this work and different illustrations will appear in: Nathan C. Carter, Richard L. Eagles, Stephen M. Grimes, Andrew C. Hahn, and Clifford A. Reiter, Chaotic Attractors with Discrete Planar Symmetry, Chaos, Solitons & Fractals [Abstract].
Images with dihedral and cyclic symmetry
1. Braid
Symmetry group C1: A chaotic attractor in the plane with no symmetry.
8.5" x 8.5" glossy paper
2. Cyclone
C8: An attractor with 8-fold cyclic symmetry.
8.5" x 7" glossy paper
3. Grand Slam
D7: An attractor with 7-fold dihedral symmetry.
14" x 13" glossy paper
Images in Frieze Patterns
4. Evening Waves
p111: An attractor with translational symmetry.
17" x 6.5" glossy paper
5. Reinventing the Wheel
p112: An attractor with half turns and translations.
17" x 6.5" glossy paper
6. Chaos Bridge, PA
pm11: An attractor with a line of reflection perpendicular to translations.
17" x 6.5" glossy paper
7A. Flies and 7B. The Third Totem Pole of Masks
p1m1: Attractors with reflections parallel to translations.
Both 17" x 6.5" glossy paper
8. Tacoma Bridge
p1a1: An attractor with glide reflections.
17" x 6.5" glossy paper
9. Bubble Trees
pma2: A p1a1 attractor with added half turns and mirror reflections.
17" x 6.5" glossy paper
10. Supernova
pmm2: An attractor with reflections perpendicular and parallel to translations.
17" x 6.5" glossy paper
Images in Wallpaper patterns
11. Oyster
p1: An attractor with two non-parallel translations.
12" x 9.5" glossy paper
12. Red Scare
p2: An attractor with two translations and half turns.
12" x 9.5" glossy paper
13. Biospheres
pm: An attractor with perpendicular translations and a reflection.
9.5" x 12" glossy paper
14. P. Guacamole
pg: An attractor with glide reflections in one direction.
10.5" x 8" glossy paper
15. Wine Glasses
cm: An attractor with reflections parallel to glide reflections.
12.5" x 12.5" glossy paper
16. Eerie eyes
pmm: An attractor with perpendicular reflections.
12.5" x 12.5" glossy paper
17. Gore
pmg: An attractor with reflections perpendicular to glide reflections. 7" x 11" glossy paper
18A. Seahorses and 18B. Heaven's Beach
pgg: Attractors with perpendicular glide reflections.
13" x 16.5" glossy paper and 62" x 18" chambray
19. Chained
cmm: An attractor with perpendicular reflections and glide reflections.
13" x 16.5" glossy paper
20. Ribbons
p4: An attractor with quarter turns.
18" x 13" glossy paper
21A. Betty and 21B. Bed of Jewels
p4m: Attractors with reflections through quarter turns.
10.5" x 6.75" glossy paper and 25" x 20.5" chambray
22. Monarchy
p4g: An attractor with glide reflections through quarter turns.
8.5" x 11" glossy paper
23. Caution: Sharp Turns
p3: An attractor with third turns.
11.5" x 10" glossy paper
24. Endless Yarn
p3m1: An attractor with all third turns on reflections.
10.5" x 6.75" glossy paper
25. Hex Weave
p31m: An attractor with some third turns on reflections.
18.5" x 23" chambray
26A. Storm and 26B. Ocean Floor
p6: Attractors with sixth turns.
12.5" x 18.5" glossy paper and 14.5" x 12.5" glossy paper
27. Basketball Dreams
p6m: An attractor with reflections on sixth turns.
15" x 13" glossy paper
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