We’ll use something a little more interesting for the array of values, we’ll define a Mandlebrot fractal function. We have build a 1,000 and 1,000 array and calculate z as a Mandlebrot function of x and y.

The heatmap is drawn with plt.imshow, and then contour lines are added with plt.contour.

See if you can follow how the arrays are built up, and the Mandlebrot function used to calculate Z, but the main purpose is to demonstrate adding contour lines to a heat map.

The Mandlebrot function may take up to 30 seconds to calculate (maybe longer on an old computer).

import numpy as np
import matplotlib.pyplot as plt
import matplotlib.cm as cm
%matplotlib inline
# Mandlebrot function - a fractal
def iter_count(c,max_iter):
x=c
for n in range(max_iter):
if abs(x)>2:
return (n)
x=x**2+c
return (max_iter)
# Build a 512 * 512 array of x, y
n=1000
max_iter=75
# xmin,xmax,ymin,ymax = -0.32,0,0.8,01.1
xmin,xmax,ymin,ymax = -0.32,0.1,0.7,1.1
x_series=np.linspace(xmin,xmax,n)
y_series=np.linspace(ymin,ymax,n)
# Create an empty array for z (which will calculated from all x and y)
z=np.empty((n,n))
# Calculate z based on the Mandlebrot function
for i,y in enumerate(y_series):
for j,x in enumerate(x_series):
z[i,j]=iter_count(complex(x,y),max_iter)
# THE CHART
# Show a grey scale heatmap with imshow
plt.imshow(z,
cmap=cm.binary,
interpolation='bicubic',
origin='lower',
extent=(xmin,xmax,ymin,ymax))
# Extent (above) defines the axes values which are not held in the
# results array (z) itself
# Add contours
levels=[2, 4, 6, 8, 10, 12, 14, 16] # Define levels
ct=plt.contour(x_series,y_series,z,levels,cmap=cm.gray)
# Add contour labels
plt.clabel(ct,fmt='%d')
plt.show()

Interests are use of simulation and machine learning in healthcare, currently working for the NHS and the University of Exeter. Committed to all work being performed in Free and Open Source Software (FOSS), and as much source data being made available as possible.
https://gitlab.com/michaelallen1966
View all posts by Michael Allen

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One thought on “50. Matplotlib: Adding contour lines to a heatmap”

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