Fractal Geometry
Sierpinski Gasket
Instructions:
- Start with an equilateral triangle and colour it completely.
- Connect the midpoints of each side of the triangle to form four smaller triangles.
- Remove the center triangle. You are now left with 3 smaller coloured triangles
- Repeat the process for every remaining coloured triangles. Find the midpoints, connect them, and remove the center.
Sierpinski Carpet
Instructions:
- Start with a square and colour it completely.
- Divide the square into a 3 by 3 grid. This gives you 9 equal sub-squares.
- Remove the center sub-square. You are left with 8 smaller coloured squares.
- Repeat the process for every remaining coloured squares.
Koch Curve
Instructions:
- Draw a straight horizontal line segment. Divide it into three equal segments.
- Remove the middle segment, and draw two sides of an equilateral triangle (forming a "bump" or "spike").
- You now have 4 smaller line segments. For every one of those segments, divide it into three equal segments, and replace the middle segment with a spike (two sides of an equilateral triangle).
- Repeat the process for every line segments.
Koch Snowflake
Instructions:
- Start with a large equilateral triangle.
- Apply the Koch curve instructions for each edge of the triangle (divide each edge it into three equal segments, and replace the middle segment with a spike, i.e.,two sides of an equilateral triangle).
- Repeat the process for every edge of the triangle.