Clustering Illusion Test

clustering_illusion.py

# 'We see patterns where they don't exist and we invent causes to explain them.' - Amos Tversky

import numpy as np

def flip(prob_same, last=None):
    
    if last is None:
        p = [.5, .5]
    elif last == 'H':
        p = [prob_same, 1 - prob_same]
    elif last == 'T':
        p = [1 - prob_same, prob_same]
    else:
        raise NotImplementedError
        
    return np.random.choice(a=['H', 'T'], p=p)

def flips(prob_same, n=30):
    
    last  = None
    flips = []

    for _ in range(n):
        last = flip(prob_same=prob_same, last=last)
        flips.append(last)

    return ''.join(flips)

print(f'1: {flips(prob_same=0.05)}')
print(f'2: {flips(prob_same=0.10)}')
print(f'3: {flips(prob_same=0.25)}')
print(f'4: {flips(prob_same=0.50)}')
print(f'5: {flips(prob_same=0.75)}')