At My Fingertips

A Sierpiński triangle is a fractal composition of equilateral triangles, where each triangle is subdivided into smaller equilateral triangles.

The Sierpinski triangle is a recursive construction. At the base case of the recursion, we want to draw an equilateral triangle.

Let's implement a function to draw an equilateral triangle with a given size (side length) and color. Use PyTamaro's triangle function for this.

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Now let's implement the recursive `sierpinski_triangle`

function.
It takes two parameters:
the side length of the Sierpinski triangle to be drawn (`size`

),
and the `limit`

for the side length, at which the recursion stops and it simply draws a normal equilateral triangle.

Each recursive function invocation composes three smaller Sierpinski triangles into a bigger Sierpinski triangle.

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Let's visualize the evolution from a normal equilateral triangle to Sierpinski triangles with growing recursion depths (smaller and smaller `limit`

values).

Write a function `evolving_triangles`

that places evolving Sierpinski trianges side-by-side.

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The shape used at the base case does not necessarily have to be a triangle. You could use a square, or a circle, or any other shape. Try it out!

The Sierpinski triangle is related to Pascal's triangle: try to color the cells of Pascal's triangle with 2^n rows if they are odd, and leave the even cells white.

This activity has been created by LuCE Research Lab and is licensed under CC BY-SA 4.0.

Sierpinski Triangle

PyTamaro is a project created by the Lugano Computing Education Research Lab at the Software Institute of USI

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