appendix_C2.py

xi_star = 0.4
max_diameter = 4


def u(xi):
    return xi_star - xi


def f1(xi):
    return (1 / (xi + 0.1)) ** 2


def f2(xi):
    return (1 / xi) ** 3


def f0(x, xi):
    if x < 0 and 0 <= xi < xi_star:
        return f1(xi)
    elif x >= 0 and xi_star <= xi < 1:
        return f2(xi)
    return 0


def f(t, x, xi):
    return f0(x - u(xi) * t, xi)


import turtle


class Pen:
    def __init__(self):
        self.pen = turtle.Pen()
        self.pen.fillcolor("")
        self.pen.color("")
        self.pen.speed(0)
        self.pen.pensize(3)

    def draw(self, x, y, xi):
        self.pen.setposition(x, y)
        self.pen.dot(xi * max_diameter, "yellow")


turtle.bgcolor("black")
turtle.tracer(0, 0)
pen = Pen()

nx = 10  # number of x intervals below and above 0
nxi = 10  # number of xi steps
nt = 20  # number of time steps
ppi = 10  # particles per interval
x_interval = (ppi + 1) * max_diameter

from numpy import linspace
import time

for t in range(nt):
    pen.pen.clear()
    for x in range(-nx, nx):
        count = 0
        for xi in linspace(0, 1, nxi):
            nr_particles = f(t, x, xi)
            for i in range(int(nr_particles)):
                pos_x = i % ppi
                if i != 0 and pos_x == 0:
                    count += 1
                pen.draw(x * x_interval + pos_x * max_diameter, count * max_diameter, xi)
            count += 1

    turtle.update()
    time.sleep(0.1)

turtle.done()

Why are you using this turtle thing at all? Isn't it better to plot publication ready graphs using matplotlib? Also, I would generally keep calculation and post-processing code separate and run them separately too. You could always save using pickle or csv modules.

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