What are fractals?What are fractals? What if you view the Lake Michigan What if you view the Lake Michigan

shoreline in Google Earth from shoreline in Google Earth from space? space?

What would you see?What would you see?

What are fractals?What are fractals?

What are fractals?What are fractals? Now, move in closer, what do you Now, move in closer, what do you

see now?see now?

What are fractals?What are fractals?

What are fractals?What are fractals? Let’s begin to make a length Let’s begin to make a length

measurement between two fixed measurement between two fixed points on the shoreline as we zoom. points on the shoreline as we zoom.

What do you think will happen to the What do you think will happen to the measurements as you zoom in closer measurements as you zoom in closer and closer? and closer?

What are fractals?What are fractals? Predict what measurement would Predict what measurement would

give you a larger quantity and why? give you a larger quantity and why?

Let’s see what happens!Let’s see what happens!

70.93 m at altitude 2.19 km70.93 m at altitude 2.19 km

73.79 m at altitude 964 m73.79 m at altitude 964 m

77.63 m at altitude 414 m77.63 m at altitude 414 m

82.75 m at altitude 268 m82.75 m at altitude 268 m

86.75 m at altitude 196 m86.75 m at altitude 196 m

What are fractals?What are fractals? What did you observe?What did you observe?

What are fractals?What are fractals? Since the coastline is jagged, you Since the coastline is jagged, you

could measure into the nooks and could measure into the nooks and crannies the closer you get to the crannies the closer you get to the ground level. ground level.

In Google Earth, the measuring tool In Google Earth, the measuring tool began measuring with a kilometer long began measuring with a kilometer long ruler.ruler.

As we zoomed, what unit ruler was As we zoomed, what unit ruler was used?used?

What are fractals?What are fractals? What unit would you use as you to What unit would you use as you to

measure if you walked the shoreline measure if you walked the shoreline and made measurements? and made measurements?

What if it was jagged at every point What if it was jagged at every point on the coastline and you measured it on the coastline and you measured it with shorter and shorter rulers? with shorter and shorter rulers?

What are fractals?What are fractals? The measurement gets longer and The measurement gets longer and

longer.longer. You could even measure it with You could even measure it with

atomically short ruler. atomically short ruler. You will now see how the coastline You will now see how the coastline

would be infinitely long.would be infinitely long.

This is a fractal! This is a fractal!

What are fractals?What are fractals? Most objects in nature aren't formed Most objects in nature aren't formed

of squares or triangles, but of more of squares or triangles, but of more complicated geometric figures. complicated geometric figures.

What are fractals?What are fractals? Many natural objects - ferns, Many natural objects - ferns,

coastlines, lungs, etc. - are shaped coastlines, lungs, etc. - are shaped like fractals.like fractals.

What are fractals?What are fractals? Fractals are irregular or fragmented Fractals are irregular or fragmented

geometric shapes that can be repeatedly geometric shapes that can be repeatedly subdivided into parts, subdivided into parts, each of which is a each of which is a smaller copy of the whole.smaller copy of the whole.

Fractals are used in computer modeling of Fractals are used in computer modeling of natural structures that do not have simple natural structures that do not have simple geometric shapes such as clouds, geometric shapes such as clouds, mountainous landscapes, and coastlines.mountainous landscapes, and coastlines.