https://www.reddit.com/r/math/comments/nt4o10

prettycool.py

# From u/42IsHoly:
# https://www.reddit.com/r/math/comments/nt4o10/a_pretty_cool_but_completely_useless_function_i/
# 
# > we can define a “pseudo-base function” which we’ll call B. B(x) = Sum (xn *
# > nth digit of x) Where the ones digit is the 0th, the tens digit is the 1st,
# > the 1/10s digit the -1st the hundreds digit the 2nd, etc.
# 
# This function assumes conversion from the decimal base, but we should be able to generalize that.
# 
# Script by u/toppletwist. 2021, public domain.

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

MAX_TERMS = 32

def to_base(base, x):
    a = []
    i = 0
    while x > 0 and i < MAX_TERMS:
        x, n = math.modf(x)
        a.append(n)
        x *= base
        i += 1
    return a

def pretty_cool(base, x):
    assert (x > 0 and x < 1), "n should be in open interval (0,1)"
    res = 0.
    b = 1.
    for digit in to_base(base, x):
        res += b * digit
        b = b / x
    return res

STEP_SIZE = .001
BASES = [1.1, 2, math.e, math.pi, 4, 8, 10, 12, 16, 32, 60]

xs = np.arange(STEP_SIZE, 1., STEP_SIZE)
for base in BASES:
    ys = list(map(lambda n: pretty_cool(base, n), xs))
    plt.plot(xs, ys, label=f"base {base}")
plt.legend()
plt.yscale('log')
plt.show()