File:Peano Curve Steinhaus 1.svg
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![File:Peano Curve Steinhaus 1.svg](https://upload.wikimedia.org/wikipedia/commons/thumb/c/c4/Peano_Curve_Steinhaus_1.svg/720px-Peano_Curve_Steinhaus_1.svg.png?20150525204038)
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[edit]DescriptionPeano Curve Steinhaus 1.svg |
English: Peano Curve Steinhaus (Level 1) |
Date | |
Source | Own work |
Author | Gjacquenot |
SVG development InfoField | ![]() This plot was created with Matplotlib. |
Source code InfoField | Python code# -*- coding: utf-8 -*-
#
# A fractal Peano curve, showing how a line
# (dimension 1) can literally fill the plane (dimension 2),
# illustrating how streams can fill a surface.
#
# http://mathworld.wolfram.com/SierpinskiCurve.html
# http://www.physics.mcgill.ca/~gang/multifrac/intro/intro.htm
#
# Guillaume Jacquenot
# 2015-05-25
# CC-BY-SA
import numpy as np
import matplotlib
from matplotlib.pyplot import figure, show, rc, grid
import random
def symmetrize(a = +1.0, b = -1.0, c = 0.0, X = [], Y = []):
# Create symmetric points over a line, that is described
# with the following equation
# ax + by + c = 0
den = 1.0/(a**2+b**2)
Xs = []
Ys = []
for x,y in zip(X,Y):
xl = den*(b**2*x-a*b*y-a*c)
yl = den*(-a*b*x+a**2*y-b*c)
Xs.append(2*xl-x)
Ys.append(2*yl-y)
return Xs,Ys
def generateSymmetries(DX, DY):
# Create symmetric pattern
DX[2] = np.flipud(-DX[1])
DY[2] = np.flipud(DY[1])
DX[3] = np.flipud(DX[1])
DY[3] = np.flipud(-DY[1])
DX[4] = np.flipud(-DX[1])
DY[4] = np.flipud(-DY[1])
def getOffset(key):
offsetX, offsetY = 0.0,0.0
for i,k in enumerate(key):
scale = 1.0/2**(i+1)
k = int(k)
if k%2==1:
offsetX += -scale
else:
offsetX += +scale
if k<3:
offsetY += +scale
else:
offsetY += -scale
return offsetX, offsetY
class Pattern(object):
def __init__(self, rootPattern_X = [-0.5,-0.5,-0.75], rootPattern_Y = [+0.0,+0.25,+0.5]):
self.level = 0
Xs,Ys = symmetrize(a = -1.0, b = -1.0, c = 0.0, X = rootPattern_X, Y = rootPattern_Y)
self.pattern_X = {1:np.append(rootPattern_X, np.flipud(Xs))}
self.pattern_Y = {1:np.append(rootPattern_Y, np.flipud(Ys))}
generateSymmetries(self.pattern_X,self.pattern_Y)
Xs,Ys = symmetrize(a = +1.0, b = -1.0, c = 1.0, X = rootPattern_X[0:-1], Y = rootPattern_Y[0:-1])
self.patternS_X = {1:np.append(rootPattern_X[0:-1], np.flipud(Xs))}
self.patternS_Y = {1:np.append(rootPattern_Y[0:-1], np.flipud(Ys))}
generateSymmetries(self.patternS_X,self.patternS_Y)
patternE_X,patternE_Y = symmetrize(a = +1.0, b = +1.0, c = 0.0, X = self.patternS_X[1], Y = self.patternS_Y[1])
self.patternE_X = {1:np.array(patternE_X)}
self.patternE_Y = {1:np.array(patternE_Y)}
generateSymmetries(self.patternE_X, self.patternE_Y)
class Steinhaus(object):
def __init__(self, level = 6, rootPattern_X = [-0.5,-0.5,-0.75], rootPattern_Y = [+0.0,+0.25,+0.5]):
self.level = level
self.pattern = Pattern(rootPattern_X, rootPattern_Y)
self.lines = {1:{str(k):self.get(k) for k in range(1,5)}}
for n in range(2,self.level+1):
self.generateLevel(n)
def generateLevel(self, level = 2):
self.lines[level] = {}
for key,lines in self.lines[level-1].iteritems():
self.lines[level].update({key+str(k):self.getFromKey(key+str(k), len(lines[0])) for k in range(1,5)})
def get(self, id, idParent = 0, level = 1, offset = (0.0, 0.0), nParent = 1):
scale = 1.0/2**(level-1)
if (id == (5-idParent)) or (nParent==2 and idParent==id):
return [[scale*self.pattern.patternS_X[id]+offset[0], scale*self.pattern.patternE_X[id]+offset[0]],\
[scale*self.pattern.patternS_Y[id]+offset[1], scale*self.pattern.patternE_Y[id]+offset[1]]]
else:
return [scale*self.pattern.pattern_X[id]+offset[0]], [scale*self.pattern.pattern_Y[id]+offset[1]]
def getFromKey(self, key, nParent = 1):
return self.get(id = int(key[-1]), idParent = int(key[-2]), level = len(key), offset = getOffset(key[:-1]), nParent = nParent)
def makePlot(self, outputFilename = r'Steinhaus.svg', level = 1, plotGrid = False, randomColor = False):
rc('grid', linewidth = 1, linestyle = '-', color = '#a0a0a0')
fig = figure()
ax = fig.add_axes([0.12, 0.12, 0.76, 0.76])
grid(plotGrid)
for lines in self.lines[level].itervalues():
for lineX,lineY in zip(lines[0],lines[1]):
if randomColor:
color = [random.random() for _ in range(3)]
else:
color = 'k'
ax.plot(lineX, lineY, lw = 1, ls = '-', color = color)
xlimMin, xlimMax = (-1.0, +1.0)
ylimMin, ylimMax = (-1.0, +1.0)
ax.set_xlim((xlimMin, xlimMax))
ax.set_ylim((ylimMin, ylimMax))
ax.set_aspect('equal')
ax.set_xticks([])
ax.set_yticks([])
fig.savefig(outputFilename)
fig.show()
if __name__ == '__main__':
s = Steinhaus()
for i in range(1,s.level+1):
s.makePlot(outputFilename = r'Steinhaus_{0}.svg'.format(i), level = i, randomColor = False)
s.makePlot(outputFilename = r'Steinhaus_{0}.png'.format(i), level = i, randomColor = False)
|
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current | 20:40, 25 May 2015 | ![]() | 720 × 540 (2 KB) | Gjacquenot (talk | contribs) | User created page with UploadWizard |
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