README_Lab3.md

Lab 3: Fractal Modeling in Spatial Systems

This lab explores fractal structures using recursive and iterative methods, highlighting their application in spatial modeling and natural pattern simulation.

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Objectives

• Implement recursive generation of the Sierpinski triangle
• Visualize fractals using matplotlib
• Study properties of self-similarity and recursive transformations
• Understand how fractals can model natural and infrastructure forms

Key Concepts

• Fractal Geometry
• Recursive Algorithms
• Affine Transformations
• Spatial Resolution & Depth Levels

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Examples

Sierpinski Triangle (Recursive)

def sierpinski(x, y, size, depth):
    if depth == 0:
        draw_triangle(x, y, size)
    else:
        new_size = size / 2
        sierpinski(x, y, new_size, depth - 1)
        sierpinski(x + new_size, y, new_size, depth - 1)
        sierpinski(x + new_size / 2, y + new_size * (3**0.5)/2, new_size, depth - 1)