Wolfram's "rule 30" cellular automaton. Read it, download it, and then execute `python rule30_animation.py` from your terminal in the same directory.

rule30_animation.py

from os import get_terminal_size
from time import sleep

terminal_size = get_terminal_size()
num_cells = terminal_size.columns # We'll have as many cells as can fit in the terminal's width
sleep_time = 4.0 / terminal_size.lines # Animation speed will be proportional to the terminal's height

# Lookup table for Wolfram's "rule 30" cellular automaton
RULE_30 = {
  (0,0,0) : 0,
  (0,0,1) : 1,
  (0,1,0) : 1,
  (0,1,1) : 1,
  (1,0,0) : 1,
  (1,0,1) : 0,
  (1,1,0) : 0,
  (1,1,1) : 0,
}

# Initialize state with a single 1 in the middle:
state = [0] * num_cells # Create a list of length "num_cells" containing all 0's.
state[num_cells // 2] = 1 # Set the middle cell to 1. If num_cells is even this will be just to the left of the middle.

while True: # "while True" means "repeat the following block forever". "while 1 == 1" would have the same effect.
  # Print current state, using spaces for 0's and rectangles for 1's. "''.join(...)" turns "['█', ' ', '█']" into "█ █".
  print(''.join([' ' if cell == 0 else '█' for cell in state]))

  # Update state by looking at each cell (at index i) and its left and right neighbors (at i-1 and i+1).
  # The first cell's (state[0]) left neighbor should be the last cell. Python handles this for us automatically by taking state[-1] to mean the last cell.
  # Similarly, the last cell's (state[num_cells-1]) right neighbor should be the first cell.
  # Python doesn't handle this for us, so we use "(i+1) % num_cells" (remainder after division) to wrap around to the beginning as needed.
  state = [RULE_30[state[i-1], state[i], state[(i+1) % num_cells]] for i in range(num_cells)] 

  # Wait a moment before the next iteration
  sleep(sleep_time)