Goursat Gewirr mit Matplotlib

English version below.

	Dieser Plot auf sämtlichen Produkten bei redbubble

German version will be follow soon. Plot of the Redbubble T-Shirt.

English Version

#!/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)