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What are fractals?

What are fractals?. What if you view the Lake Michigan shoreline in Google Earth from space? What would you see?. What are fractals?. What are fractals?. Now, move in closer, what do you see now?. What are fractals?. What are fractals?.

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What are fractals?

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  1. What are fractals? • What if you view the Lake Michigan shoreline in Google Earth from space? What would you see?

  2. What are fractals?

  3. What are fractals? • Now, move in closer, what do you see now?

  4. What are fractals?

  5. What are fractals? • Let’s begin to make a length measurement between two fixed points on the shoreline as we zoom. • What do you think will happen to the measurements as you zoom in closer and closer?

  6. What are fractals? • Predict what measurement would give you a larger quantity and why? Let’s see what happens!

  7. 70.93 m at altitude 2.19 km

  8. 73.79 m at altitude 964 m

  9. 77.63 m at altitude 414 m

  10. 82.75 m at altitude 268 m

  11. 86.75 m at altitude 196 m

  12. What are fractals? • What did you observe?

  13. What are fractals? • Since the coastline is jagged, you could measure into the nooks and crannies the closer you get to the ground level. • In Google Earth, the measuring tool began measuring with a kilometer long ruler. • As we zoomed, what unit ruler was used?

  14. What are fractals? • What unit would you use as you to measure if you walked the shoreline and made measurements? • What if it was jagged at every point on the coastline and you measured it with shorter and shorter rulers?

  15. What are fractals? • The measurement gets longer and longer. • You could even measure it with atomically short ruler. • You will now see how the coastline would be infinitely long. This is a fractal!

  16. What are fractals? • Most objects in nature aren't formed of squares or triangles, but of more complicated geometric figures.

  17. What are fractals? • Many natural objects - ferns, coastlines, lungs, etc. - are shaped like fractals.

  18. What are fractals? • Fractals are irregular or fragmented geometric shapes that can be repeatedly subdivided into parts, each of which is a smaller copy of the whole. • Fractals are used in computer modeling of natural structures that do not have simple geometric shapes such as clouds, mountainous landscapes, and coastlines.

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