Unit 4

Physical and Chemical Branching Structures

Copper sulfate electrochemical deposition viewed through a microscope

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Sections:

4.1 - Growing Rough Patterns: Electrodeposition

4.2 - More on Fractal Dimension

4.3 - Modeling Fractal Growth

4.4 - Viscous Fingering

4.5 - Why Do Viscous Fingers Branch?

4.6 - What Do You Think?

4.7 - Research Projects

Earlier we noted that "No two coastlines are ever exactly the same; neither are two snowflakes or two lightning bolts. Though two such patterns may have the same overall shape, if you look closely you will see that they differ in the details of their structure. The same is true for other natural fractals as well. Each example is unique¼''

Now we make another observation. If two fractals are of the same class (e.g., two bolts of lightning), they will be somehow similar in appearance to each other.

What is the basis of that similarity? How can we describe, classify, and measure different random fractal patterns in nature? That is the subject of this unit and the activities described on the following pages.

Q4.1: In the color insert there are several pictures of fractal structures. How are these objects similar to each other in appearance? In what ways do they look different?

Q4.2: There are many ways to rank objects. For example, you can line up students according to weight. Or you can line them up by height, shoe size, age, or hair color. Look at the photographs and figure out different ways to line up these images in order. Line them up according to as many different criteria as you can think of. How inventive can you be?

Q4.3: The pictures show very different objects, yet their images look rather similar in many ways. Why do you think these objects look so much alike? What are possible ways that their similarity might arise from a common cause?

The following set of activities will help you to: (i) describe aggregates and random fractals; (ii) model the aggregation process by which the structures grow; and (iii) recognize and measure the basic properties of random fractals.

Previous: 3.10 - Research Projects

Next: 4.1 - Electrodeposition