Tessellations of Kleinian Groups.
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2 years ago
Parabolic Sunrise
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Technically a kaleidoscope sequence using a non-euclidean symmetry. But to me it evokes an other-worldly sunrise. For more info, see http://brainjam.ca/tessellations.htm.
Peter Liepa
1 year ago
Kleinian Group Limit Set
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Limit set for a Kleinian group. The corresponding tessellation is shown in low contrast. The limit set is just the parts of the tessellation where the tiles get very small. The limit set is black and […]
Peter Liepa Math and Animation
2 years ago
Kaleidoscope with Two Parabolic Generators
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The underlying group has two parabolic generators, and the tessellation is equivalent to a checkboard that has been inverted in a circle centered at the origin. By animating the tiles, we get a (non-euclidean) […]
Peter Liepa Math and Animation
2 years ago
A Degenerating Group
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Shows the tessellation for a group which is evolving towards being singly degenerate. Corresponds to Figure 10.9 in the book Indra's Pearls. The parameter is evolving from (t_a,t_b)=(1.97-0.866,1.97-0.866) […]
Peter Liepa Math and Animation
2 years ago
Quasifuchsian Zoom Out
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A zoom out for the tessellation corresponding to the group defined in Grandma's Recipe in the book Indra's Pearls. (t_a,t_b)=(1.95+0.02i, 3). For more information see http://www.brainjam.ca/tessellations.htm.
Peter Liepa Math and Animation
2 years ago
Unwinding an Apollonian Gasket
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A Grandma's Recipe group evolving from (t_a,t_b)=(2,2) to (t_a,t_b)=(2+1.2i,3). There is a freeze frame at about the 6sec mark where (t_a,t_b)=(2+0.1i,3). This corresponds to Figure 8.7 in the book Indra's […]
Peter Liepa Math and Animation
2 years ago
Quasifuchsian Zoom
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A zoom into the tessellation corresponding to Figure 8.1 in Indra's Pearls. The group is defined according to "Grandma's Recipe" with parameters t_a = t_b = 1.87+0.1i, and has two generators. The tiles […]
Peter Liepa Math and Animation
2 years ago
An Apollonian Gasket Unwinding
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Grandma's recipe group evolving from (t_a,t_b)=(2,2) to (t_a,t_b)=(2,2+1.275i). The first frame is an Apollonian gasket, the final frame is a quasifuchsian group tessellation. For more information see […]
Peter Liepa Math and Animation
2 years ago
Zoom into an Apollonian Packing
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A zoom into the tessellation corresponding to a punctured torus group with Maskit parameter 2. This is an Apollonian packing, with tiles either filled in with text, or with a purple/magenta coloring. The […]
Peter Liepa Math and Animation
2 years ago
Evolving Punctured Torus Tessellation
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Tessellation for the continuously evolving punctured torus groups as the Maskit parameter μ goes from 2 to 2+2i. For more information see http://www.brainjam.ca/tessellations.htm.
Peter Liepa Math and Animation
2 years ago
Zoom on an Evolving Punctured Torus Group
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This is a zoom on the tessellation corresponding to a punctured torus group as its Maskit parameter μ evolves from 2 to 2+2i. For more information see http://www.brainjam.ca/tessellations.htm.
Peter Liepa Math and Animation
2 years ago
Evolution Toward a Doubly Parabolic Group
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This is an evolution toward the punctured torus group with Maskit parameter mu=1.64213876+0.76658841i, as described in Figures 9.3 and 9.4 of the book Indra's Pearls. The final configuration is a circle […]
Peter Liepa Math and Animation

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