Also how do I find numbers in Julias set? what number is in between an escapee and a prisoner?

To find numbers in the Julia set, you need to understand how the Julia set is defined. The Julia set is a fractal generated by iterating a complex number equation. Each point in the complex plane is classified as either an "escapee" or a "prisoner" based on whether it remains bounded or escapes to infinity after a certain number of iterations.

To find numbers in the Julia set, you can use software or programming languages that have built-in functions for generating fractals. One popular choice is to use a programming language like Python with libraries such as NumPy and Matplotlib. Here's a simple example of generating and plotting the Julia set using Python:

1. Install Python: If you don't have Python installed, download and install it from the official website (https://www.python.org/downloads/). Make sure to choose the appropriate version for your operating system.

2. Install the required libraries: Open your command prompt (Windows) or terminal (macOS/Linux) and run the following commands to install the required libraries:
```
pip install numpy matplotlib
```

3. Write the code: Create a new Python file (e.g., "julia_set.py") and open it in a text editor. Copy and paste the following code:

```python
import numpy as np
import matplotlib.pyplot as plt

def julia_set(xmin, xmax, ymin, ymax, width, height, max_iterations):
x = np.linspace(xmin, xmax, width)
y = np.linspace(ymin, ymax, height)
c = complex(-0.8, 0.156) # Change this complex number to explore different Julia sets

x, y = np.meshgrid(x, y)
z = x + 1j * y
img = np.zeros_like(z, dtype=int)

for i in range(max_iterations):
mask = np.abs(z) <= 2
img[mask] = i
z[mask] = z[mask] ** 2 + c

return img

# Set the desired parameters
xmin, xmax = -2, 2
ymin, ymax = -2, 2
width, height = 800, 800
max_iterations = 100

# Generate the Julia set
image = julia_set(xmin, xmax, ymin, ymax, width, height, max_iterations)

# Plot the Julia set
plt.imshow(image, cmap='jet', extent=[xmin, xmax, ymin, ymax])
plt.colorbar()
plt.title("Julia Set")
plt.show()
```

4. Run the code: Save the Python file and run it using the command prompt or terminal:
```
python julia_set.py
```

The code will generate a plot showing the Julia set within the specified range. You can modify the parameters like `xmin`, `xmax`, `ymin`, `ymax`, and `max_iterations` to explore different regions and levels of detail within the Julia set.

As for finding the number between an escapee and a prisoner in the Julia set, it is important to note that the Julia set is a highly complex fractal with infinitely many points. Each point is either an escapee or a prisoner depending on the number of iterations. There is no specific number that exists directly between an escapee and a prisoner in the Julia set. Instead, the set is classified as a whole based on the behavior of these points.