File:Domain coloring.png
Domain_coloring.png (536 × 534 pixels, file size: 530 KB, MIME type: image/png)
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Summary edit
DescriptionDomain coloring.png |
English: Original image was made with Gimp-2.2 and Michael J. Gruber's conformal.py plugin, available here. Rays and grid added to simulate the color function of en:File:Domain coloring x2-1 x-2-i x-2-i d x2+2+2i.xcf. Created for article en:Domain_coloring. It shows a discontinuous color function that also shows white rays for arguments in intervals of π/6 radians and a gray grid for equal real and imaginary values. In the graph, each discontinuity occurs when the conjugation of n equals 2 to the n, for integers n. |
Date | |
Source | File:Unit_circle_domain_coloring.png |
Author | Tryptographer at English Wikipedia |
Permission (Reusing this file) |
File:Unit circle domain coloring.png |
PNG development InfoField |
Public domainPublic domainfalsefalse |
This work has been released into the public domain by its author, Tryptographer at English Wikipedia. This applies worldwide. In some countries this may not be legally possible; if so: Tryptographer at English Wikipedia grants anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law. Public domainPublic domainfalsefalse |
Licensing edit
Public domainPublic domainfalsefalse |
This work is ineligible for copyright and therefore in the public domain because it consists entirely of information that is common property and contains no original authorship. |
Python src code edit
#!/usr/bin/env python
# conformal.py
# Copyright (C) 2006-2011 Michael J. Gruber <conformal@drmicha.warpmail.net>
#
# This program is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, version 2 of the License.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program; if not, write to the Free Software
# Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
confversion = "0.3+"
# allow access through module and without
import math, cmath
from math import *
from cmath import *
from array import array
from gimpfu import *
# try importing typical math modules
try:
from fpconst import *
import scipy.special
except ImportError:
pass
try:
import mpmath
except ImportError:
pass
def conformal_batch(width, height, code, constraint, xl, xr, yt, yb, grid, checkboard, gradient, filename):
conformal_core(width, height, code, constraint, xl, xr, yt, yb, grid, checkboard, gradient, filename)
def conformal(width, height, code, constraint, xl, xr, yt, yb, grid, checkboard, gradient):
conformal_core(width, height, code, constraint, xl, xr, yt, yb, grid, checkboard, gradient, None)
def conformal_core(width, height, code, constraint, xl, xr, yt, yb, grid, checkboard, gradient, filename):
image = gimp.Image(width, height, RGB)
drawables = [ gimp.Layer(image, "Argument", width, height, RGBA_IMAGE, 100, NORMAL_MODE),
gimp.Layer(image, "Log. modulus", width, height, RGBA_IMAGE, 35, VALUE_MODE),
gimp.Layer(image, "Grid", width, height, RGBA_IMAGE, 10, DARKEN_ONLY_MODE)]
image.disable_undo()
l = 1
for drawable in drawables:
image.add_layer(drawable, l)
l = -1
bpp = drawables[0].bpp
gimp.tile_cache_ntiles(2 * (width + 63) / 64)
dest_rgns = [ drawable.get_pixel_rgn(0, 0, width, height, True, False) for drawable in drawables ]
progress = 0
max_progress = width * height
if filename is None:
gimp.progress_init("Conformally Mapping...")
sx = (width-1.0)/(xr-xl)
sy = (height-1.0)/(yt-yb)
w = complex(0.0)
z = complex(0.0)
cx, cy = 0, 0
mp2 = 2.0*math.pi # no need to do this 500*500 times...
ml2 = 2.0*math.log(2) # no need to do this 500*500 times...
ml = math.log(2) # no need to do this 500*500 times...
compiled=compile(code, "compiled code", "exec", 0, 1)
compiledconstraint=compile(constraint, "compiled constraint code", "exec", 0, 1)
dests = [ array("B", "\x00" * width*height*bpp) for i in range(3) ]
QUANT = 4096
args = [ i/(QUANT-1.0) for i in range(QUANT) ]
arggradsamples = list(gimp.gradient_get_custom_samples(gradient, args)) + [[0,]*bpp]
modgradsamples = list(gimp.gradient_get_custom_samples("Default", args)) + [[0,]*bpp]
sqrsamples = [ [0,]*(bpp-1) + [255,], [255,]*(bpp-1) + [255,] , [0,]*bpp ]
for col in range(QUANT+1):
arggradsamples[col] = [ ((int)(255*arggradsamples[col][i]+0.5)) for i in range(bpp)]
modgradsamples[col] = [ ((int)(255*modgradsamples[col][i]+0.5)) for i in range(bpp)]
qinf = 1.0 + 1.0/(QUANT-1) # uggely uggely
args = [0.0,] * width
mods = [0.0,] * width
sqrs = [0,] * width
for row in range(0, height):
for col in range(0, width):
z = col/sx + xl + 1j*( yt - row/sy)
p = True
try:
exec(compiledconstraint)
except (OverflowError, ValueError):
p = False
if not p:
w = 0.0
else:
try:
exec(compiled)
except (OverflowError, ValueError):
p = False
if not p or isnan(w) or isinf(w):
w = 0.0
try:
logw = cmath.log(w)
arg = logw.imag
if isnan(arg) or isinf(arg):
arg = 0.0
p = False
elif arg < 0.0:
arg = arg + mp2
mod = ( logw.real/ml ) % 1.0
if isnan(mod) or isinf(mod):
mod = 0.0
p = False
except (OverflowError, ValueError):
arg = 0.0
mod = 0.0
p = False
arg = arg/mp2
try:
sqr = int(w.imag/grid % 2.0) + int(w.real/grid % 2.0)
if isnan(sqr) or isinf(sqr):
sqr = 0
p = False
except (OverflowError, ValueError):
sqr = 0
p = False
sqr = sqr % 2
if not p:
arg = qinf
mod = qinf
sqr = 2
args[col] = arg
mods[col] = mod
sqrs[col] = sqr
dests[0][row*width*bpp : (row+1)*width*bpp] = array("B", [ arggradsamples [int((QUANT-1)*args[col]+0.5)][i] for col in range(0, width) for i in range(bpp) ] )
dests[1][row*width*bpp : (row+1)*width*bpp] = array("B", [ modgradsamples[int((QUANT-1)*mods[col]+0.5)][i] for col in range(0, width) for i in range(bpp) ] )
dests[2][row*width*bpp : (row+1)*width*bpp]= array("B", [ sqrsamples[sqrs[col]][i] for col in range(0,width) for i in range(bpp) ] )
progress = progress + width
if filename is None:
gimp.progress_update(float(progress) / max_progress)
for i in range(3):
dest_rgns[i][0:width, 0:height] = dests[i].tostring()
for drawable in drawables:
drawable.flush()
drawable.update(0,0,width,height)
if not checkboard:
pdb.plug_in_edge(image,drawables[2], 10, 0, 0) # amount, WRAP, SOBEL
pdb.plug_in_vinvert(image,drawables[2])
if image.parasite_find("gimp-comment"):
image.parasite.detach("gimp-comment")
image.attach_new_parasite("gimp-comment", PARASITE_PERSISTENT, """# conformal %s
code = \"\"\"
%s
\"\"\"
constraint = \"\"\"
%s
\"\"\"
xl = %f
xr = %f
yt = %f
yb = %f
grid = %f
checkboard = %d
gradient = "%s"
width = %d
height = %d
""" % (confversion, code, constraint, xl, xr, yt, yb, grid, checkboard, gradient, width, height))
if filename is None:
image.enable_undo()
gimp.Display(image)
gimp.displays_flush
else:
if filename.find('.xcf') > 0:
pdb.gimp_xcf_save(1, image, drawables[0], filename, filename)
else:
flat_layer = pdb.gimp_image_flatten(image)
pdb.gimp_file_save(image, flat_layer, filename, filename)
register(
"conformal_batch",
"Colour representation of a conformal map",
"Colour representation of a conformal map",
"Michael J Gruber",
"Michael J Gruber",
"2011",
"",
"",
[
(PF_INT, "width", "width", 512),
(PF_INT, "height", "height", 512),
(PF_TEXT, "code", "code", "w=z"),
(PF_TEXT, "constraint", "constraint", "p=True"),
(PF_FLOAT, "xl", "x left", -1.0),
(PF_FLOAT, "xr", "x right", 1.0),
(PF_FLOAT, "yt", "y top", 1.0),
(PF_FLOAT, "yb", "y bottom", -1.0),
(PF_FLOAT, "grid", "grid spacing", 1.0),
(PF_BOOL, "checkboard", "checker board grid", 0),
(PF_GRADIENT, "gradient", "gradient", "Full saturation spectrum CCW"),
(PF_FILE, "file", "file", "out.xcf.bz2"),
],
[],
conformal_batch)
register(
"conformal",
"Colour representation of a conformal map",
"Colour representation of a conformal map",
"Michael J Gruber",
"Michael J Gruber",
"2012",
"<Toolbox>/File/Create/_Conformal ...",
"",
[
(PF_INT, "width", "width", 512),
(PF_INT, "height", "height", 512),
(PF_TEXT, "code", "code", "w=z"),
(PF_TEXT, "constraint", "constraint", "p=True"),
(PF_FLOAT, "xl", "x left", -1.0),
(PF_FLOAT, "xr", "x right", 1.0),
(PF_FLOAT, "yt", "y top", 1.0),
(PF_FLOAT, "yb", "y bottom", -1.0),
(PF_FLOAT, "grid", "grid spacing", 1.0),
(PF_BOOL, "checkboard", "checker board grid", 0),
(PF_GRADIENT, "gradient", "gradient", "Full saturation spectrum CCW"),
],
[],
conformal)
main()
File history
Click on a date/time to view the file as it appeared at that time.
Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 21:13, 13 December 2018 | 536 × 534 (530 KB) | IntegralPython (talk | contribs) | Cropped white room on the sides off. | |
21:04, 13 December 2018 | 346 × 346 (112 KB) | IntegralPython (talk | contribs) | Cropped out the text information that is better described shown in the description itself, not in the picture | ||
02:11, 25 December 2017 | 733 × 524 (168 KB) | SebastianHelm (talk | contribs) | {{subst:Upload marker added by en.wp UW}} {{Information |Description = {{en|Original image was made with Gimp-2.2 and Michael J. Gruber's conformal.py plugin, available here: http://www.analysis.uni-hannover.de/~gruber/Computing/Conformal/. Rays and gr... |
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