Goursat Gewirr mit Matplotlib
English version below.
Dieser Plot auf sämtlichen Produkten bei redbubble | ||
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German version will be follow soon. Plot of the Redbubble T-Shirt.
English Version |
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#!/usr/bin/env python print("This will maybe take a while, depending on the figure dpi you have chosen and your system performance") # inspired by: https://stackoverflow.com/a/4687582/9479418 # import necessary libarys from mpl_toolkits.mplot3d import axes3d import matplotlib.pyplot as plt import numpy as np # activare the output into the jupyter notebook %matplotlib inline # ploting an implicit function # for more info: https://en.wikipedia.org/wiki/Implicit_function def plot_implicit(fn, bbox=(-2.5,2.5)): ''' create a plot of an implicit function fn ...implicit function (plot where fn==0) bbox ..the x,y,and z limits of plotted interval''' xmin, xmax, ymin, ymax, zmin, zmax = bbox*3 fig = plt.figure(dpi=500) ax = fig.add_subplot(111, projection='3d') ax.set_title('$Wired$ $Goursat$ $Tanglecube$') A = np.linspace(xmin, xmax, 100) # resolution of the contour B = np.linspace(xmin, xmax, 15) # number of slices A1,A2 = np.meshgrid(A,A) # grid on which the contour is plotted for z in B: # plot contours in the XY plane X,Y = A1,A2 Z = fn(X,Y,z) cset = ax.contour(X, Y, Z+z, [z], zdir='z', colors=('k', (1, 1, 1)), linewidths = 0.5) # [z] defines the only level to plot for this contour for this value of z for y in B: # plot contours in the XZ plane X,Z = A1,A2 Y = fn(X,y,Z) cset = ax.contour(X, Y+y, Z, [y], zdir='y', colors=('k', (1, 1, 1)), linewidths = 0.5) for x in B: # plot contours in the YZ plane Y,Z = A1,A2 X = fn(x,Y,Z) cset = ax.contour(X+x, Y, Z, [x], zdir='x', colors=('k', (1, 1, 1)), linewidths = 0.5) # must set plot limits because the contour will likely extend # way beyond the displayed level. Otherwise matplotlib extends the plot limits # to encompass all values in the contour. ax.set_zlim3d(zmin,zmax) ax.set_xlim3d(xmin,xmax) ax.set_ylim3d(ymin,ymax) # deactivae coordinate axis rendering plt.axis('off') # save the plot to the file "wired_torus" plt.savefig("goursat_tangle.png", bbox_inches='tight') # output plt.show() # mathematical function for the Goursat Tangle # for more info: https://en.wikipedia.org/wiki/%C3%89douard_Goursat def goursat_tangle(x,y,z): a,b,c = 0.0,-5.0,11.8 return x**4+y**4+z**4+a*(x**2+y**2+z**2)**2+b*(x**2+y**2+z**2)+c plot_implicit(goursat_tangle)