Koch snowflake

Simple Python/Tkinter visualization of the Koch snowflake fractal.

Developed to explore, understand, and teach how fractals work.

What It Does

The script starts from a single equilateral triangle and recursively transforms each edge into four smaller segments, producing the classic Koch snowflake pattern. The drawing is animated so you can watch the fractal emerge step by step.

Highlights:

• recursive edge subdivision
• equilateral triangle point construction
• animated rendering on a Tkinter.Canvas
• rainbow coloring for the final recursion level
• optional labels for selected iteration counts

Requirements

• Python 3
• Tkinter support in your Python installation

Run

python snowflake.py

A window will open and begin drawing the snowflake after a short delay.

How It Works

The main flow in snowflake.py is:

1. create a base equilateral triangle
2. split each edge into thirds
3. build the outward peak of a smaller equilateral triangle on the middle third
4. recurse into the four resulting edge segments
5. draw the deepest-level segments to visualize the fractal

Important functions:

• thirds(p1, p2) computes the one-third and two-third points of a segment
• get_3rd_point(p1, p2, o) finds the third vertex of an equilateral triangle
• process_edge(canvas, p1, p2) performs the recursive Koch edge construction
• triangle(canvas, p1, p2) creates the initial triangle and starts the recursion

Tuning The Visualization

You can experiment by editing these values in snowflake.py:

• max_level controls recursion depth
• p1 and p2 control the size and position of the starting triangle
• w inside process_edge() changes the orientation behavior and can produce alternate shapes such as an anti-snowflake
• time.sleep(0.01) controls drawing speed

Notes

• Higher recursion levels increase the number of drawn segments quickly.
• The script uses global counters to track the current recursion depth and drawing iteration.
• This project is best suited for learning, experimentation, and visual explanation rather than performance-heavy rendering.

Images