Discover the beauty of the Mandelbrot Set with TensorFlow

The Mandelbrot set is a famous mathematical concept that can be represented as a visual image. It is a set of complex numbers that satisfies certain conditions related to a mathematical function called the “Mandelbrot function.” This function is defined by the equation:

z = z^2 + c

where z and c are complex numbers. It is a set of all complex numbers c for which the sequence z_0, z_1, z_2, … defined by this equation remains bounded as the number of iterations increases. In other words, the sequence doesn’t tend towards infinity.

To visualize the Mandelbrot set, you can use a computer to compute the value of z for each point on a grid of complex numbers, and then color each point based on whether or not it belongs to the Mandelbrot set or not.

Here is an example of how you might generate a visual representation of the Mandelbrot set using TensorFlow:

import tensorflow as tf

# Set up the grid of complex numbers
re_min, re_max = -2, 1
im_min, im_max = -1, 1
re_vals = tf.linspace(re_min, re_max, 1000)
im_vals = tf.linspace(im_min, im_max, 1000)
re_grid, im_grid = tf.meshgrid(re_vals, im_vals)
c = tf.complex(re_grid, im_grid)

# Iterate the Mandelbrot function
z = tf.zeros_like(c)
magnitude = tf.zeros_like(c, dtype=tf.float32)
for i in range(200):
  z = z*z + c
  magnitude = tf.abs(z)
  escaped = tf.greater(magnitude, 4.0)

# Create a color map based on the number of iterations
colors = tf.where(escaped, tf.ones_like(magnitude), tf.zeros_like(magnitude))
colormap = tf.stack([colors, colors, colors], axis=-1)

# Display the image
plt.imshow(colormap)
plt.show()

This code generates a grid of complex numbers, then applies the Mandelbrot function to each point in the grid. It counts the number of iterations until the magnitude of the result becomes greater than 4.0, and uses this number to color each point. Finally, it displays the image using a colormap that shows the points in the Mandelbrot set in black and the points outside the set in white.