Try the suggestions below, design your own, or write an essay using any of the questions throughout this unit as inspiration.

Pattern Formation

Now you have the tools needed to carry out your own investigations of electrodeposition and Hele-Shaw experiments and to investigate for yourself the computer programs. We suggest that you work with a small group and go through the following steps.

1 Think of a variation of the experiment or settings of the computer program (or, best of all, a comparison between the two).


2. Think about the results you expect to observe with your proposed experiment. Draw the expected pattern.


3. Submit a written proposal to your teacher, describing the experiment and the expected result. Your teacher will check if it is promising, the availability of needed components, and will evaluate its safety.


4. After approval, carry out the experiment and compare results with your predictions. Does your outcome warrant further investigations? Where will they lead?

Electrochemical Deposition

Here are some possible variations of the electrodeposition experiment:

(a) Variations of the solution concentration.


(b) Changing the salt in solution. Try using CuCl or ZnCl or AgNO₃ or tin salts.


(c) Varying the position of the negative terminal relative to the positive terminal.


(d) Using more than one negative terminal.


(e) Making uneven the spacing between the cell plates. This can be done by inserting a stack of cover slips, or equivalent, in one corner of the cell.


(f) Run at constant current rather than constant voltage. Can you estimate what range of currents will lead to a reasonable growth rate? See if your estimated current results in a change in aggregate shape or rate of growth.

Viscous Fingering

Here are some possible variations of the Hele-Shaw experiment that you can try:

(a) Inject air into as 50-50 mixture of air and glycerol.


(b) Inject oil into glycerol.


(c) Inject very concentrated sugar water into pure water, and vice versa. Do you observe anything in this case?


(d) Try placing a grooved plate between the plates of the Hele-Shaw cell and then performing the viscous fingering experiment. Can you predict what will happen?


(e) Try the Greased Lightning experiment. On a plate of plastic 3 or 4 cm on an edge, put a spot of lithium grease (a lubricant available at hardware and automobile supply stores). The spot should be about 1/2 cm in diameter. Place a second plastic plate over the first and squeeze the plates just above the spot as hard as you can. The grease will spread thinly between the plates. Can you predict the shape of the grease as it spreads? Will it finger? Now release the pressure on the grease slowly, and then gradually pull the plates apart. Can you explain the remaining pattern?


Repeat this experiment with a drop of model paint. Or with thick chocolate frosting. Or with toothpaste.

Other Research

Assemble a collection of images that may be fractals: river deltas, leaf veins, lightning strokes, nerve cells, root systems, and so forth. Estimate the fractal dimension of each one. If possible, scan the image into the computer and use the Fractal Dimension program to measure its dimension. Compare the result with your estimate.

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