Heatmap with matplotlib using matshow

I am trying to generate a heatmap of a 10x10 matrix. All values in the matrix are probabilities; sum of all elements equal to 1.0. I decided to use the matshow plot type (it seemed easy to use), however I cannot generate the output I'd like to have so far. 1.Visually it looks kinda ugly. Would you recommend a fitting color map for use in a heatmap? 2.Is there a way to assign predefined bins to the color map when using matshow? E.g. take a gradient of 1000 colors, always use the same colors for the corresponding probabilities. In default behavior, I think matshow checks the minimum and maximum values, assigned the first and last colors in the gradient to those values, then colorizes the values in between by interpolation. Sometimes I have very similar probabilities in the matrix, and other times the range of probabilities may be great. Due to the default behavior I tried to explain above, I get similar plots, which makes comparisons harder. My code for generating the said heat maps (and an example plot) is below by the way. Thanks! ``` import numpy as np import matplotlib import matplotlib.pyplot as plt def pickcoord(): i = np.random.randint(0,10) j = np.random.randint(0,10) return [i,j] board = np.zeros((10,10)) for i in range(1000000): try: direction = np.random.randint(0,2) new_board = np.zeros((10,10)) coords = pickcoord() if direction == 1: for k in range(2): new_board[coords[0]][coords[1]+k] = 1 else: for k in range(2): new_board[coords[0]+k][coords[1]] = 1 except IndexError: new_board = np.zeros((10,10)) board = board + new_board board_prob = board/np.sum(board) plt.figure(figsize=(6,6)) plt.matshow(board_prob, cmap=matplotlib.cm.Spectral_r, interpolation='none') plt.xticks(np.arange(0.5,10.5), []) plt.yticks(np.arange(0.5,10.5), []) plt.grid() ```