For https://medium.com/@Vlad_Zamfir/simple-model-of-an-internal-pow-attacker-1a713cf00672 comment

internal-attacker.py

#!/usr/bin/env python

import matplotlib.pyplot as plot


# time "steps", e.g. months
n = 50

# hashing power pre-attack: using "honest miners" as base unit
x0 = 0
y0 = 1

# part of honest mining power that the attacker "buys into"
P = [0.01, 0.02, 0.05, 0.1]

# rate of increase (1 == no change)
h = 1.05
R = [h * r for r in [1.05, 1.1, 1.25]]



def expgen(start, rate):
    current = start
    while True:
        (yield current)
        current = current * rate
    return


ygen = expgen(y0, h)
ygen.send(None)
Y = [y0, *[ygen.send(None) for _ in range(n)]]

for p in P:
    x1 = y0*p
    for i, r in enumerate(R):
        xgen = expgen(x1, r)
        xgen.send(None)
        X = [0, x1, *[xgen.send(None) for _ in range(n-1)]]

        l = 'X, ' + 'r == ' + str(round(r, 3)) + ', p == ' + str(p) + ', a == ' + str(round(r/h, 3))
        plot.plot(X, marker = str(i+1), markersize = 10, label = l)

# PLOT

plot.plot(Y, marker = 'o', label = 'Y, ' + 'h == ' + str(h))
plot.xlabel('n (time period)')
plot.ylabel('Xn and Yn (hashing power)')
plot.ylim((0, 15))
plot.legend()
plot.grid()
plot.show()