Peter Liepa

@peterliepa

Visual math, mainly geometry -- euclidean, hyperbolic, projective, conformal, computational.

Toronto
Vrijeme pridruživanja: svibanj 2009.

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  1. 7. pro 2019.

    Live version and code at . (Doesn't work well on iPhone Safari, but what else is new.) 3/3

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  2. 7. pro 2019.

    The gradient used is the gradient of the angle ACB for two fixed points A and B. That's an unusual gradient, with a funky formula, but the circular trajectories follow from the fact that inscribed angles in a circle subtended by the same chord (AB here) are equal. 2/3

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  3. 7. pro 2019.

    A gradient flow where the trajectories form orthogonal sets of coaxial circles. Some liberties taken in this visualization, because particles flow in both directions along flow lines and level sets. (short thread)

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  4. 4. pro 2019.

    of the Hesse Transfer Principle in Richter-Gebert's Perspectives on Projective Geometry. 2/2

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  5. 4. pro 2019.

    Projective geometry is endlessly fascinating. The six points of a complete quadrilateral (blue) are centrally projected to a conic. The images of opposite points define 3 lines (green) that are concurrent (as indicated by the red arrow). Based on an illustration 1/2

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  6. 18. ruj 2019.

    Conformal mappings for the given pictures are normalized Jacobi sn, inverse stereoscopic, cos+i sin, and a frequency modulated version of cos+i sin. These were rendered in online Mathematica and have some artifacts. 3/3

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  7. 18. ruj 2019.

    To compute these neighborhoods, find a conformal mapping that takes a real interval (or the entire real axis) to the circle, and then map the image of a grid containing the domain. (This of course can be generalized with maps to any curve) 2/3

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  8. 18. ruj 2019.

    Conformal neighborhoods of circles and subcircles. I.e. square grids that follow the curve. Square size depends on arc speed of underlying parameterization. Grid on one side of the curve is Schwarz reflection of grid on the other side, which here is inversion in the circle. 1/3

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  9. 9. kol 2019.

    I feel this way about math (especially geometry): "Writing songs is a great thing. It's like a jigsaw puzzle and a kaleidoscope put together" -

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  10. 1. kol 2019.

    [2/2]: A Riemann sphere tessellated by a packing of hyperbolic tessellations. Induced by a Kleinian reflection group whose limit set is a Sierpinski circle packing. Other visualizations by Chéritat are at and

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  11. 1. kol 2019.

    [1/2]: Planet Chéritat - . Webgl implementation of "a Kleinian reflection group with a Sierpinski limit set" devised by Arnaud Chéritat ( )

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  12. 24. lip 2019.

    Oddly satisfying contrail doodler. (requires a mouse).

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  13. 13. lip 2019.

    From the archives, vintage 2010. A hyperbolic tiling mapped to the exterior of a filled Julia set. Frames from a zoom sequence -- wide shot, mid-zoom, closeup.

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  14. proslijedio/la je Tweet

    Elegant proof that the square root of 2 is irrational, by Stanley Tennenbaum & see the interesting comments & links

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  15. proslijedio/la je Tweet
    7. lip 2019.
    Odgovor korisniku/ci

    This is a version showing particle trails. Perhaps not exactly what you were requesting, but it gives an idea of how particles move approximately along geodesics.

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  16. 5. lip 2019.

    Hyperbolic billiards. A close-up.

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  17. 5. lip 2019.

    Hyperbolic billiards. Elastic collisions with clumping. There are really only three balls - black, green, blue.

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  18. 23. svi 2019.

    I'm working on a hyperbolic doodler -- an online paint program for triangle group tessellations. Here are some test images. Wabi-sabi meets the hyperbolic plane meets webgl.

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  19. 8. svi 2019.

    Conformal morph of rectangle to the unit disk. Via Jacobi sn(). Created using and

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  20. 8. svi 2019.

    Conformal mapping of rectangles of varying aspect ratio (w/h) to the unit disk. Via Jacobi sn(). Created using and

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