Fractals

Transcript

Fractals WHAT IS A FRACTAL? A never-ending pattern where the parts look like the whole.A fractal is a never-ending pattern. In regular geometry, if you zoom in close enough to the edge of a circle, the curve eventually flattens out and just looks like a straight line. But if you zoom in on a fractal, the pattern never smooths out. Instead, you will see the exact same complex shapes repeating over and over again, shrinking down infinitely. The Magic Word: Self-Similarity The most important rule of a fractal is self-similarity. This means a small part of the shape is a miniature, perfectly scaled copy of the whole shape. Think of a tree. A tree has a main trunk that splits into big branches. Those big branches split into smaller branches, and those split into even smaller twigs. If you snap off one small branch and hold it upright, it looks just like a tiny version of the entire tree. Fractals in the Wild You don't just find fractals in math textbooks; they are all over nature. You can spot them in: Ferns: Look closely at a single frond on a fern. It is made of smaller leaves that look exactly like the main frond. Lightning: A bolt of lightning branches out in a jagged, repeating fractal pattern as it strikes. Snowflakes: As ice crystals form, the points of a snowflake branch off into smaller, identical geometric points. Your Body: The tubes inside your lungs (bronchi) and your blood vessels branch out in a fractal pattern. This allows your body to pack a massive amount of surface area into a very small space to help you breathe and circulate blood efficiently.