Colormap with maximum distinguishable colours

Question

Using matplotlib in Python I\'m plotting anywhere between 20 and 50 lines. Using matplotlib\'s sliding colour scales these become indistinguishable after a certain number of li

Answer 1

I loved the idea of palette created by @xuancong84 and modified his code a bit to make it not depending on alpha channel. I drop it here for others to use, thank you @xuancong84!

import math

import numpy as np
from matplotlib.colors import ListedColormap
from matplotlib.cm import hsv


def generate_colormap(number_of_distinct_colors: int = 80):
    if number_of_distinct_colors == 0:
        number_of_distinct_colors = 80

    number_of_shades = 7
    number_of_distinct_colors_with_multiply_of_shades = int(math.ceil(number_of_distinct_colors / number_of_shades) * number_of_shades)

    # Create an array with uniformly drawn floats taken from <0, 1) partition
    linearly_distributed_nums = np.arange(number_of_distinct_colors_with_multiply_of_shades) / number_of_distinct_colors_with_multiply_of_shades

    # We are going to reorganise monotonically growing numbers in such way that there will be single array with saw-like pattern
    #     but each saw tooth is slightly higher than the one before
    # First divide linearly_distributed_nums into number_of_shades sub-arrays containing linearly distributed numbers
    arr_by_shade_rows = linearly_distributed_nums.reshape(number_of_shades, number_of_distinct_colors_with_multiply_of_shades // number_of_shades)

    # Transpose the above matrix (columns become rows) - as a result each row contains saw tooth with values slightly higher than row above
    arr_by_shade_columns = arr_by_shade_rows.T

    # Keep number of saw teeth for later
    number_of_partitions = arr_by_shade_columns.shape[0]

    # Flatten the above matrix - join each row into single array
    nums_distributed_like_rising_saw = arr_by_shade_columns.reshape(-1)

    # HSV colour map is cyclic (https://matplotlib.org/tutorials/colors/colormaps.html#cyclic), we'll use this property
    initial_cm = hsv(nums_distributed_like_rising_saw)

    lower_partitions_half = number_of_partitions // 2
    upper_partitions_half = number_of_partitions - lower_partitions_half

    # Modify lower half in such way that colours towards beginning of partition are darker
    # First colours are affected more, colours closer to the middle are affected less
    lower_half = lower_partitions_half * number_of_shades
    for i in range(3):
        initial_cm[0:lower_half, i] *= np.arange(0.2, 1, 0.8/lower_half)

    # Modify second half in such way that colours towards end of partition are less intense and brighter
    # Colours closer to the middle are affected less, colours closer to the end are affected more
    for i in range(3):
        for j in range(upper_partitions_half):
            modifier = np.ones(number_of_shades) - initial_cm[lower_half + j * number_of_shades: lower_half + (j + 1) * number_of_shades, i]
            modifier = j * modifier / upper_partitions_half
            initial_cm[lower_half + j * number_of_shades: lower_half + (j + 1) * number_of_shades, i] += modifier

    return ListedColormap(initial_cm)

These are the colours I get:

from matplotlib import pyplot as plt
import numpy as np

N = 16
M = 7
H = np.arange(N*M).reshape([N,M])
fig = plt.figure(figsize=(10, 10))
ax = plt.pcolor(H, cmap=generate_colormap(N*M))
plt.show()