Innovation

%pip install ipywidgets

import numpy as np
import matplotlib.pyplot as plt
from ipywidgets import interact, interactive
from IPython.display import display

import numpy as np

from matplotlib import pyplot as plt

def plot(growth_rate=0.3, kind = 'innovation'):
    a0 = 1  # initial amount of innovation
    r = growth_rate / 365  # growth rate per annum
    T = 365 * 30  # days of simulation
    Tdel = 365  # days of delay
    a = np.zeros(T)  # amount of innovation without delay
    adel = np.zeros(T)  # amount of innovation with delay
    a[0] = a0
    adel[0] = a0

    for t in range(1, T):
        a[t] = a[t - 1] + a[t - 1] * r
        if t < Tdel + 1:
            adel[t] = adel[t - 1]
        else:
            adel[t] = adel[t - 1] + adel[t - Tdel - 1] * r

    # plot innovation as a function of time
    time = np.arange(1, T + 1)
    years = time / 365

    if (kind == 'innovation'):
        plt.figure()
        plt.plot(years, a, 'k')
        plt.plot(years, adel, 'r')
        plt.xlabel('years')
        plt.ylabel('accumulated innovation')
    else:
        # plot time to a given amount of innovation
        plt.figure()
        plt.plot(a, years, 'k')
        plt.plot(adel, years, 'r')
        plt.xlim([0, 1000])
        plt.xlabel('required innovation')
        plt.ylabel('years to achievement')

    plt.show()

w = interactive(plot, growth_rate=(0.1,0.5,0.01), kind=["innovation", "achievement"])
display(w)