# complex gamma function # color plot  import math, cmath from cmath import exp, sin, cos from math import pi, tanh from scipy.special import gamma import numpy as np from numpy import vectorize  import matplotlib as mp import matplotlib.pyplot as plot from colorsys import hls_to_rgb  # line width of the frame grid lw_grid=2  # color of the axes axes_color = [0.28,0.28,0.26]  # lightness gradient Lgrad = 0.5  # number of iterations #  100: preview # 1000: publication N = 100  # viewport X=[-6,6] Y=[-6,6]  # function to be graphed def f1(z):   return gamma(z)    style = {   "axes.linewidth": lw_grid } mp.rcParams.update(style)    def colorize(z):   n,m = z.shape   c = np.zeros((n,m,3))   c[np.isinf(z)] = (1.0, 1.0, 1.0)   c[np.isnan(z)] = (0.5, 0.5, 0.5)   idx = ~(np.isinf(z) + np.isnan(z))    # hue   H = 1.0-np.angle(z[idx])/(2*pi)    # lightness   L = 0.03+0.97*(1.0 - 1.0/(1.0+abs(z[idx])**Lgrad))   # L = L*(1-0.9*np.cos(pi/2*np.log2(abs(z[idx])))**80)    c[idx] = [hls_to_rgb(h,l,1.0) for h,l in zip(H,L)]   return c  fig = plot.figure() ax = fig.add_subplot(1,1,1) ax.spines['bottom'].set_color(axes_color) ax.spines['top'].set_color(axes_color)  ax.spines['right'].set_color(axes_color) ax.spines['left'].set_color(axes_color)  ax.xaxis.set_tick_params(width=lw_grid,length=-6,pad=10,color=axes_color) ax.yaxis.set_tick_params(width=lw_grid,length=-6,pad=10,color=axes_color) ax.set_aspect('equal') ax.axis(X+Y) ax.set_xticks(range(X[0],X[1]+1,1)) ax.set_yticks(range(Y[0],Y[1]+1,1))  axis_x = np.linspace(X[0],X[1],N) axis_y = np.linspace(Y[0],Y[1],N) x,y = np.meshgrid(axis_x,axis_y) z = x - y*1j  w = np.zeros((N,N),dtype='complex') w = vectorize(f1)(z).conj()  # interpolation='bicubic' ax.imshow(colorize(w), interpolation='none',   extent=(X[0],X[1],Y[0],Y[1]))  # contour lines ax.contour(x, -y, abs(w), [0.5,1,2,6,24],   colors="#404040", alpha=0.2, linewidths=[3.5,4,4,4,4]) ax.contour(x, -y, abs(w), [1E-9,1E-8,1E-7,1E-6,1E-5,0.0001,0.001],   colors="#404040", alpha=0.1, linewidths=3) ax.contour(x, -y, abs(w), [0.01,0.1],   colors="#404040", alpha=0.2, linewidths=[3.8,3.8])  ax.text(2.47, 1.2,"1", fontsize=10, color="#404040") ax.text(2.97, 0.5,"2", fontsize=10, color="#404040") ax.text(4.02, 1.0,"6", fontsize=10, color="#404040") ax.text(4.8, 0.4,"24", fontsize=10, color="#404040")  ax.text(0.3,-0.2, "2", fontsize=10, color="#404040") ax.text(0.5,-0.6, "1", fontsize=10, color="#404040") ax.text(0.3,-1.1, "1/2", fontsize=10, color="#404040") ax.text(-0.1,-2.0,"1/10", fontsize=10, color="#303030") ax.text(-0.6,-3.1,"1/100", fontsize=10, color="#404040") ax.text(-1.1,-4.1,"1/1000", fontsize=10, color="#303030") ax.text(-1.4,-5.1,"1/10000", fontsize=10, color="#202020")  plot.savefig("gamma.jpg",bbox_inches='tight')