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## Problem: Write a program that uses recursion to calculate dynamical systems such as the Lorenz attractor, Belousov-Zhabotinsky reaction, and visualize them using Turtle Graphics.

## Solution

###
**Step 1: Set up the Environment**

First, we need to install the Turtle Graphics library, which comes with Python by default. We can start by creating a new Python script, let’s call it “dynamical_systems.py”.

###
**Step 2: Define the Dynamical Systems Equations**

Let’s pick the Lorenz attractor as an example. Define the Lorenz equations within a function. These equations represent the dynamics of a chaotic system:

```
def lorenz_equations(x, y, z):
sigma = 10
rho = 28
beta = 8/3
dx_dt = sigma * (y - x)
dy_dt = x * (rho - z) - y
dz_dt = x * y - beta * z
return dx_dt, dy_dt, dz_dt
```

**Step 3: Implement Recursive Visualization**

Now, let’s create a function to visualize the Lorenz attractor using Turtle Graphics:

```
import turtle
def draw_lorenz(x, y, z, steps):
turtle.penup()
turtle.goto(x, z)
turtle.pendown()
for _ in range(steps):
dx, dy, dz = lorenz_equations(x, y, z)
x, y, z = x + dx * 0.01, y + dy * 0.01, z + dz * 0.01
screen_x, screen_z = 10*x, 10*z
turtle.goto(screen_x, screen_z)
turtle.done()
if __name__ == "__main__":
draw_lorenz(1, 0, 0, 1000)
```

This script sets up the Turtle Graphics window and uses the recursive function to calculate the Lorenz attractor’s trajectory and visualize it on the screen.