Q4.28: You have just discovered how a random walker can be used to grow spidery patterns similar to those found in nature. Does this mean that random processes are actually involved in forming these objects in nature? Or are lightning, nerve cells, termite tunnels, and electrodeposition patterns formed by totally different processes, processes that have nothing to do with random walkers?

Q4.28: The discovery that a random walker can be used to grow spidery patterns similar to structures found in nature is very important to scientists. Why do you think this discovery is important? In what ways could this discovery prove to be useful?

Q4.28: Write a brief statement predicting the value of the fractal dimension of the patterns that result under each of the following conditions and giving the reasons for your prediction:

(a) inject air into glycerol


(b) inject water at higher pressure into glycerol


(c) inject a 50-50 mix of water and glycerol into pure glycerol