fun facts about fractals (mathematics)

[still]

snowflakes (along with many other natural phenomena) are examples of fractals, or shapes that replicate the same pattern at increasingly small scales. in other words, if you were to zoom in on a fractal forever, you could always see the same pattern no matter how zoomed in you are.

here's how to construct a fractal called a Koch Snowflake which looks a little like a snowflake:
1. Draw a triangle with three sides of equal length.
2. On each of its sides, divide the side into three equal segments. Take the middle segment and construct another equilateral triangle using the middle segment as its base. Repeat this with every side, and you should now a total of six smaller triangles.
3. Take your six new triangles and repeat step 2. So your six triangles now make a total of 18 smaller triangles.
4. Repeat this an infinite number of times. Now you have a shape with the same triangular pattern on infinitesimally small scales.