File:Kleinian group limit set on sphere.png
From Wikibooks, open books for an open world
Jump to navigation
Jump to search
Size of this preview: 600 × 600 pixels. Other resolutions: 240 × 240 pixels | 480 × 480 pixels | 1,000 × 1,000 pixels.
Original file (1,000 × 1,000 pixels, file size: 20 KB, MIME type: image/png)
This is a file from the Wikimedia Commons. The description on its description page there is shown below. |
Contents
Summary
DescriptionKleinian group limit set on sphere.png |
English: Kleinian group limit set on sphere |
Date | |
Source | Made with program Lim Version 2.2[1] by Curtis T McMullen |
Author | Adam majewski |
Other versions |
|
File:Kleinian group limit set on sphere.svg is a vector version of this file. It should be used in place of this PNG file when not inferior.
File:Kleinian group limit set on sphere.png → File:Kleinian group limit set on sphere.svg
For more information, see Help:SVG.
|
Licensing
I, the copyright holder of this work, hereby publish it under the following license:
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
bash src code
Part of readme file
The program lim draws the orbits of circles under the action of a group of Mobius transformations. Usage: lim [options] -a [agree] circles are regarded the same if center and radius differ by less than epsilon/agree. -b put box around image -c [c.x c.y r] clipping circle -d [depth] - generations -e [epsilon] - radius of circles to ignore -h [huge-radius] huge cutoff radius -l [linewidth] - in 1/72nd of inch -m [maximum] number of circles to draw -q quiet -s plot on sphere -t [gray] make sphere transparent. Circles on the back colored gray (0-1.0). -w [xmin ymin xmax ymax] window < data.file > postscript.file Entries in the data.file are of the following forms: c center-x center-y radius for circle in the limit set r center-x center-y radius for reflection in the group m ax ay bx by cx cy dx dy for mobius transformation in the group t ax ay bx by cx cy dx dy for mobius transformation to be applied to the coordinate system u cx cy r for reflection in a circle to be applied to the coordinate system
# cusp.run file from Lim Version 2.2 by Copyright (c) 2001 Curtis T McMullen
#
# Classic maskit boundary picture: on sphere
#
# mu=1.91I 0.05
#
./lim -s -d 60 -e 0.0001 <<eof > cusp.ps
c 0. 0. 1
m 1 1 0 1 0 -1 1 -1
m 1 -1 0 -1 0 1 1 1
m 0.955 -0.025 0.045 0.025 -1.955 0.025 0.955 -0.025
m 0.955 -0.025 -0.045 -0.025 1.955 -0.025 0.955 -0.025
eof
converion from ps to png file :
pstopnm -xborder=0 -yborder=0 -xsize=1000 -ysize=1000 cusp.ps
pnmtopng cusp001.ppm >cuspb.png
references
Items portrayed in this file
depicts
some value
5 September 2017
image/png
File history
Click on a date/time to view the file as it appeared at that time.
Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 14:40, 5 September 2017 | 1,000 × 1,000 (20 KB) | Soul windsurfer | User created page with UploadWizard |
File usage
The following page uses this file: