Generate smoke/genie shape randomly in Python

Question

I want to produce shapes like these in Python:

#  # # #  #
  #   #
        # #  
     # #
  #
   #

   # # # #   #
#   # #
   #   #
         #  
     #
   #
      #

x items scattered across a grid height × width randomly, with a greater probability to appear in the topmost rows, and most likely to be near but offset from the previous row in each new row.

I can only think of trying to align bell curve-shaped distributions for each row, and offset the mean by a little bit from the previous row's for the next row's. What might be a less mathematical and more programmatic and readable solution?

Answer 1

I had a play and came up with the following code:

import numpy as np

def smokey_motif(rows: int, cols: int) -> str:
    # convolution used for next row
    # a bit of smoothing and edge detection seems good
    conv = np.array([1, 2, 0, 2, 1])
    # generating rows in reverse order, starting with
    # a single particle somewhere near the middle
    row = np.zeros(cols, dtype=int)
    row[np.random.binomial(cols, 0.5)] = 1
    result = [row]
    for _ in range(rows):
        # add some randomness into state after smoothing 
        state = np.convolve(row, conv, 'same') * np.random.uniform(0.5, 2, row.shape)
        # increase number of particles a bit
        n = sum(row) + np.random.binomial(2, 0.2)
        row = np.zeros_like(row)
        row[np.argsort(-state)[:n]] = 1
        result.append(row)
    # turn arrays of numbers into a string
    return '\n'.join(
        ' '.join(' #'[v] for v in row)
        for row in reversed(result)
    )

np.random.seed(3)
print(smokey_motif(8, 8))

producing:

#   #   #   #  
  #   #   #    
    #   #   #  
      #   #   #
        #   #  
          #    
        #      
      #        
        #      

I found it easier to start from the bottom, and playing with the constants gives quite a bit of control which could obviously be exposed by turning into parameters. It'll produce something weird occasionally, but produces something nice the majority of the time.