Work on illustrations for John Parker's upcoming book "Complex Hyperbolic Kleinian Groups".
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Math -
ComplexHyperbolic09
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Written by Anton
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Tuesday, 07 July 2009 05:49 |
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New in this edition: C-spheres
In general, a C-sphere is a surface in the boundary of hyperbolic space that is topologically a sphere and is foliated by chains (C-circles). One way to specify a C-circle is to give a path in homogeneous coordinates that provides vectors that are normal to the chains. The left picture is given by the path  = ( -t^3, \sqrt{2}, t) "\gamma(t) = ( -t^3, \sqrt{2}, t)")
The points corresponding to  are  "(\pm 1, 0, 0)") . Taking them to  "(0,0,\pm 1)") produces the picture on the right. Note: the notebook ComplexHyperbolic0.5 did not draw correct C-spheres, so it's no longer available. The code for the images above will be in CH0.6. |
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Last Updated on Monday, 20 July 2009 15:17 |
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Math -
ComplexHyperbolic09
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Written by Anton
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Tuesday, 30 June 2009 04:43 |
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New in ComplexHyperbolic0.4nb: - The animation of extors changing type (shown in CH0.3.nb post)
- A GenerateGroup command for iterating matrix group generators
- An example of using R-Balls to build fundamental domains.
The new notebook: ComplexHyperbolic0.4.nb. |
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Read more... [complexhyperbolic0.4.nb]
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Math -
ComplexHyperbolic09
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Written by Anton
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Tuesday, 23 June 2009 04:57 |
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The notebook has been updated with a proper routine for the Clifford Torus animation (see CH0.2.nb), a quick description of extors, and an animation showing a spinal sphere turning into a fan and then into a Clifford torus. ComplexHyperbolic0.3.nb (right click to play) |
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Last Updated on Wednesday, 24 June 2009 19:32 |
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Read more... [ComplexHyperbolic0.3.nb]
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Math -
ComplexHyperbolic09
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Written by Anton
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Tuesday, 16 June 2009 04:20 |
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The notebook now has the routines for drawing fans and Clifford tori, objects defined similarly to the spinal spheres: |
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Last Updated on Friday, 19 June 2009 17:47 |
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Read more... [ComplexHyperbolic0.2.nb]
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Math -
ComplexHyperbolic09
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Written by Anton
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Tuesday, 02 June 2009 04:53 |
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Here are some sample pictures ComplexHyperbolic0.1.nb can produce. I'll post better ones later write about the various objects. Cygan Spheres (unit sphere translated, various spheres, various spheres not around 0) |
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Last Updated on Tuesday, 02 June 2009 05:32 |
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Read more... [Some Pictures]
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