File:Quadratic-function-z2-minus4z-plus5.jpg
Summary
| Description |
English: Quadratic function f(z) := z2−4z+5. |
| Date | |
| Source | Own work |
| Author | Rumil |
Licensing
I, the copyright holder of this work, hereby publish it under the following license:
  |
This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication. |
| The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.
|
Source code
import math, cmath
from cmath import exp, sin, cos
from math import pi, tanh
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=[-2,6]
Y=[-4,4]
# function to be graphed
def f1(z):
return z*z-4*z+5
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 = (1.0 - 1.0/(1.0+abs(z[idx])**Lgrad))
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()
ax.imshow(colorize(w), interpolation='none',
extent=(X[0],X[1],Y[0],Y[1]))
# contour lines
cl = ax.contour(x, -y, abs(w), [1,2,5,10],
colors="#606060", alpha=0.4, linewidths=3.2)
ax.clabel(cl, inline=1, fontsize=16, fmt="%g", colors="#000000",
manual=[[1,-3.2],[1.4,-2.3],[1.8,-1.6],[1.5,-1.2]])
plot.savefig("plot.jpg",bbox_inches='tight')