limited_growth

# Computes and plots a sequence y[n] which grows from an initial value
# y[0] towards a boundary value G, depending on the growth factor q
# Copyright 2024 Roland Richter                          [Mu: Python 3]

import matplotlib.pyplot as plt

G = 5000
q = 0.19
n_generations = 50

y = n_generations * ['?']

y[0] = 75.0

for n in range(n_generations-1):
    y[n+1] = y[n] + q * (G - y[n])  # limited growth
    # y[n+1] = y[n] + q/G * y[n] * (G - y[n])   # logistic growth

# print(y)

# Define the x and y coordinates of the points
x = [k for k in range(n_generations)]

# Create a new plot
plt.figure()

# Plot the points using the 'o' symbol
plt.plot(x, y, 'o')

# Set the title and labels for the x and y axes
plt.title('Growth')
plt.xlabel('time')
plt.ylabel('n')

# Show the plot
plt.show()

# ----------------------------------------------------------------------
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program.  If not, see <https://www.gnu.org/licenses/>.