Barnsley Fern Generator in Python

B/Barnsley Fern/README.md

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+# Barnsley Fern using Turtle Graphics
+
+This Python script generates the Barnsley Fern fractal using the Turtle Graphics library. The Barnsley Fern is a famous fractal pattern created through mathematical transformations. 
+
+![Barnsley Fern](Fern.png)
+
+## How to Run
+
+1. Ensure you have Python and the Turtle Graphics library installed in your environment.
+2. Clone this repository or download the Python script to your computer.
+3. Run the script using your preferred Python environment.
+
+## About the Fern
+
+The Barnsley Fern is created by applying four transformations with specific probabilities:
+
+1. Transformation 1: Probability 1%
+2. Transformation 2: Probability 85%
+3. Transformation 3: Probability 7%
+4. Transformation 4: Probability 7%
+
+Each transformation corresponds to a specific set of equations that determine the position of the points.
+
+## Customize the Fern
+
+You can customize various aspects of the generated fern:
+
+- Screen size and background color
+- Dot color and size
+- Number of iterations
+
+## Example
+
+```python
+# Customize the screen size and other parameters
+screen.setup(width=800, height=800)
+screen.bgcolor("black")
+
+# Customize the dot color and size
+fern.dot(2, "green")
+
+# Set the number of iterations
+iterations = 100000

S/sierpinski_triangle/README.md

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+# Sierpiński Triangle Generator using Turtle Graphics
+
+This Python script generates the Sierpiński Triangle fractal using the Turtle Graphics library. The Sierpiński Triangle is a classic example of a fractal pattern known for its self-replicating, intricate structure.
+
+![Sierpiński Triangle](sierpinski_triangle.png)
+
+## How to Run
+
+1. Ensure you have Python and the Turtle Graphics library installed in your environment.
+2. Clone this repository or download the Python script to your computer.
+3. Run the script using your preferred Python environment.
+
+## About the Sierpiński Triangle
+
+The Sierpiński Triangle is constructed by recursively removing smaller equilateral triangles from a larger equilateral triangle. This process is repeated infinitely, resulting in a self-replicating pattern.
+
+## Customize the Triangle
+
+You can customize various aspects of the generated Sierpiński Triangle:
+
+- Depth of recursion to control the complexity of the pattern.
+- Initial size of the triangle.
+- Choose whether to display a rainbow-colored triangle or a white one.
+
+## Example
+
+```python
+# Customize the depth of recursion and other parameters
+depth = 3
+initial_size = 400
+rainbow = False  # Set to True for a rainbow-colored triangle
+
+# Run the script to generate the Sierpiński Triangle

S/sierpinski_triangle/sierpinski_triangle.py

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+import turtle
+import random
+
+p = [[0, 280], [-242, -140], [242, -140]]
+colors = [
+    ((255, 0, 0), (0, 69)),
+    ((255, 127, 0), (69, 69 * 2)),
+    ((255, 255, 0), (69 * 2, 69 * 3)),
+    ((0, 255, 0), (69 * 3, 69 * 4)),
+    ((0, 0, 255), (69 * 4, 69 * 5)),
+    ((75, 0, 130), (69 * 5, 69 * 6)),
+    ((148, 0, 211), (69 * 6, 69 * 7))
+]
+
+def changeColor(x):
+    colorx = (x + 242)
+    for i, (color, (start, end)) in enumerate(colors):
+        if start <= colorx < end:
+            t.pencolor(color)
+            break
+
+# Set True for rainbow-colored triangle
+rainbow = False
+
+# Initialize turtle
+t = turtle.Turtle()
+t.hideturtle()
+t.speed(0)
+t.penup()
+t.pencolor('white')
+
+# Initialize screen
+s = turtle.getscreen()
+s.setup(width=600, height=600)
+s.bgcolor('black')
+
+# Draw first 3 points
+for i in range(3):
+    t.goto(p[i][0], p[i][1])
+    t.dot()
+
+# Draw 10000 points
+for i in range(10000):
+    r = random.randint(0, 2)
+    pos = t.pos()
+    # Midway points
+    x, y = (pos[0] + p[r][0]) / 2, (pos[1] + p[r][1]) / 2
+    t.goto(x, y)
+    if rainbow:
+        changeColor(x)
+    t.dot()
+
+turtle.exitonclick()

animation.py

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+import matplotlib.pyplot as plt
+from matplotlib.animation import FuncAnimation
+
+# Create a figure and axis
+fig, ax = plt.subplots()
+
+# Initialize an empty plot
+line, = ax.plot([], [], lw=2)
+
+# Set the axis limits
+ax.set_xlim(0, 2 * 3.14)
+ax.set_ylim(-1, 1)
+
+# Function to initialize the plot
+def init():
+    line.set_data([], [])
+    return line,
+
+# Function to update the plot in each frame
+def update(frame):
+    x = 2 * 3.14 * frame / 100
+    y = 0.5 * (1 + frame / 100)
+    line.set_data(x, y)
+    return line,
+
+# Create an animation
+ani = FuncAnimation(fig, update, frames=100, init_func=init, blit=True)
+
+# Display the animation (this may vary depending on your Python environment)
+plt.show()