File:Hyperbolic rotation.gif

Hyperbolic_rotation.gif(512 × 512 pixels, file size: 24 KB, MIME type: image/gif, looped, 18 frames, 4.0 s)

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Summary

Description Hyperbolic sectors of equal area are permuted by hyperbolic rotation to 10 positions. This animated GIF was requested at http://en.wikipedia.org/w/index.php?title=Wikipedia:Graphics_Lab/Illustration_workshop&diff=prev&oldid=1299170533 .
Source Own work
Author Cmglee

Python source code

#!/usr/bin/env python
PATH_INKSCAPE = r'C:\APP\inkscape122\bin\inkscape.exe'
DIR_OUT       = r'F:\gif'
WIDTH_OUT     = 512
SCALE         = 100
N_FRAME       = 10
FORMAT_SVG    = '''\
<?xml version="1.0"?>
<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" viewBox="-10 -290 300 300">
 <circle r="999" fill="#fff"/>
 <g fill="none" stroke="#000">
  <path id="axis" d="M -9,0 H 288 m -7,-4 l 7,4 l -7,4"/>
  <use xlink:href="#axis" transform="matrix(0,-1 1,0 0,0)"/>
  <path d="{out_d}" fill="#fc0"/>
  <path d="M 5,-2000 Q 0,-360 50,-200 C 70,-114 114,-70 200,-50 Q 360,0 2000,-5" fill="#fff"/>
 </g>
</svg>
'''
import re, math, subprocess
def system(command, cwd='./', is_verbose=False):
 if is_verbose: print('%s %s' % (cwd, command))
 return subprocess.Popen(command, stdout=subprocess.PIPE, cwd=cwd,
                         shell=True).communicate()[0].decode('utf-8')
def fmt(string): ## string.format(**vars()) using tags {expression!format} by CMG Lee
 def f(tag): i_sep = tag.rfind('!'); return (re.sub('\.0$', '', str(eval(tag[1:-1])))
  if (i_sep < 0) else ('{:%s}' % tag[i_sep + 1:-1]).format(eval(tag[1:i_sep])))
 return (re.sub(r'(?<!{){[^{}]+}', lambda m:f(m.group()), string)
         .replace('{{', '{').replace('}}', '}'))

path_prefix = r'%s\%s' % (DIR_OUT, os.path.basename(os.path.splitext(__file__)[0]))
for n in range(N_FRAME):
 a        = math.exp(n / 5.0 - 1)
 b        = math.exp(n / 5.0 - 0.8)
 out_d    = 'M %.0f,%.0f L 0,0 L %.0f,%.0f' % (SCALE * a, -SCALE / a,
                                               SCALE * b, -SCALE / b)
 path_svg = '%s%02d.svg' % (path_prefix, n)
 path_png = '%s%02d.png' % (path_prefix, n)
 with open(path_svg, 'w') as f: f.write(fmt(FORMAT_SVG))
 system('%s -o %s -w %d %s' % (PATH_INKSCAPE, path_png, WIDTH_OUT, path_svg), is_verbose=True)
for n in range(1, N_FRAME - 1):
 path_svg = '%s%02d.svg' % (path_prefix, n)
 path_png = '%s%02d.png' % (path_prefix, N_FRAME * 2 - 2 - n)
 system('%s -o %s -w %d %s' % (PATH_INKSCAPE, path_png, WIDTH_OUT, path_svg), is_verbose=True)
## Then drag PNGs into http://ezgif.com/maker and then Optimize at Compression
##  level: 200, Eliminate local color tables, Reduce the number of colors to 4

Licensing

I, the copyright holder of this work, hereby publish it under the following licenses:
w:en:Creative Commons
attribution share alike
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
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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.
GNU head Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.
You may select the license of your choice.

Captions

Hyperbolic sectors of equal area are permuted by hyperbolic rotation to 10 positions.

Items portrayed in this file

depicts

24,189 byte

512 pixel

512 pixel

image/gif

3ad6c4011c067ca64552035d08f3c366f5dc4333

File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeDimensionsUserComment
current08:04, 19 July 2025512 × 512 (24 KB)CmgleeLinger on end stops

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