Normalizing data and applying colormap results in rotated image using matplotlib?

Question

So I wanted to see if I could make fractal flames using matplotlib and figured a good test would be the sierpinski triangle. I modified a working version I had that simply performed the chaos game by normalizing the x range from -2, 2 to 0, 400 and the y range from 0, 2 to 0, 200. I also truncated the x and y coordinates to 2 decimal places and multiplied by 100 so that the coordinates could be put in to a matrix that I could apply a color map to. Here's the code I'm working on right now (please forgive the messiness):

import numpy as np
import matplotlib.pyplot as plt
import math
import random

def f(x, y, n):
    N = np.array([[x, y]])

    M = np.array([[1/2.0, 0], [0, 1/2.0]])

    b = np.array([[.5], [0]])
    b2 = np.array([[0], [.5]])

    if n == 0:
        return np.dot(M, N.T)

    elif n == 1:
       return np.dot(M, N.T) + 2*b

    elif n == 2:
        return np.dot(M, N.T) + 2*b2

    elif n == 3:
        return np.dot(M, N.T) - 2*b

def norm_x(n, minX_1, maxX_1, minX_2, maxX_2):
    rng = maxX_1 - minX_1
    n = (n - minX_1) / rng

    rng_2 = maxX_2 - minX_2
    n = (n * rng_2) + minX_2

    return n

def norm_y(n, minY_1, maxY_1, minY_2, maxY_2):
    rng = maxY_1 - minY_1
    n = (n - minY_1) / rng

    rng_2 = maxY_2 - minY_2
    n = (n * rng_2) + minY_2

    return n    

# Plot ranges
x_min, x_max = -2.0, 2.0
y_min, y_max = 0, 2.0

# Even intervals for points to compute orbits of
x_range = np.arange(x_min, x_max, (x_max - x_min) / 400.0)
y_range = np.arange(y_min, y_max, (y_max - y_min) / 200.0)

mat = np.zeros((len(x_range) + 1, len(y_range) + 1))   

random.seed()

x = 1
y = 1

for i in range(0, 100000):
    n = random.randint(0, 3)
    V = f(x, y, n)

    x = V.item(0)
    y = V.item(1)

    mat[norm_x(x, -2, 2, 0, 400), norm_y(y, 0, 2, 0, 200)] += 50

plt.xlabel('x0')
plt.ylabel('y')
fig = plt.figure(figsize=(10,10))
plt.imshow(mat, cmap="spectral", extent=[-2,2, 0, 2])
plt.show()

The mathematics seem solid here so I suspect something weird is going on with how I'm handling where things should go into the 'mat' matrix and how the values in there correspond to the colormap.

Answer 1

If I understood your problem correctly, you need to transpose your matrix using the method .T. So just replace

fig = plt.figure(figsize=(10,10))
plt.imshow(mat, cmap="spectral", extent=[-2,2, 0, 2])
plt.show()

by

fig = plt.figure(figsize=(10,10))
ax = gca()
ax.imshow(mat.T, cmap="spectral", extent=[-2,2, 0, 2], origin="bottom")
plt.show()

The argument origin=bottom tells to imshow to have the origin of your matrix at the bottom of the figure.

Hope it helps.