Hyperbolization on a Squircular Continuum

These videos accompany the paper: "Hyperbolization on a Squircular Continuum".

video#1: Morphing the Poincare disk to the conformal square

video#2: Morphing rectangular imagery to elliptical regions

For best results, please watch these videos in full screen mode.

The paper is available for download here

http://archive.bridgesmathart.org/2019/bridges2019-83.html

Hyperbolic Stop Signs

tiling the hyperbolic plane with stop signs

Stop signs tiling the Poincare disk

Schwarz-Christoffel mapping to conformal square

FG-Squircular mapping

Elliptical Grid mapping

Tapered2 Squircular mapping

This pattern was used in my Bridges 2018 conference paper: "A Poor Man's Hyperbolic Square Mapping" coauthored with Douglas Dunham

http://archive.bridgesmathart.org/2018/bridges2018-59.html

presentation slides in

https://www.slideshare.net/chamb3rlain/a-poor-mans-hyperbolic-square-mapping

Marcia Marcia Marcia!

Circularized Brady Bunch, Take 2.
Rest in Peace, Florence Henderson (1934-2016)

Square Brady Bunch

Schwarz-Christoffel mapping

FG-squircular mapping

elliptical grid mapping

Shirley-Chiu concentric map

Jyvaskylan Yliopisto

The University of Jyvaskyla was the venue for the Bridges Math Conference 2016 where I presented the paper "The Conformal Hyperbolic Square and Its Ilk".

The presentation slides are available here: http://www.slideshare.net/chamb3rlain/the-conformal-hyperbolic-square-and-its-ilk

You can download the paper here: http://archive.bridgesmathart.org/2016/bridges2016-179.html

Universitas Jyvaskylaensis logo

Schwarz-Christoffel mapping

FG-squircular mapping

elliptical grid mapping

Shirley-Chiu concentric map

Escher's "Circle Limit I" as a square

The 1st of Escher's 4 Circle Limits converted to a square

Escher's Circle Limit I

Schwarz-Christoffel mapping to the conformal square

FG-Squircular mapping

Elliptical grid mapping

Shirley-Chiu concentric map

Circular Scrabble boards

Scrabble board converted to a circular disc

input: Scrabble board

Schwarz-Christoffel mapping

FG-squircular mapping

elliptical grid mapping

Shirley-Chiu concentric map

Social Media Squares

actually, social media circles

input files: Social media squares

Schwarz-Christoffel mapping

FG-squircular mapping

elliptical grid mapping

Shirley-Chiu mapping