Summary

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.
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https://creativecommons.org/licenses/by-sa/4.0CC BY-SA 4.0 Creative Commons Attribution-Share Alike 4.0 truetrue

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

conversion from ps to png file :

pstopnm -xborder=0 -yborder=0 -xsize=1000 -ysize=1000 cusp.ps
pnmtopng cusp001.ppm >cuspb.png

From png to svg using Image Magic

 convert cusp.png cusp.svg

Optimisation using svgo

references

1. ↑ Programs by Curtis T McMullen