Morphogenesis by the mechanism of Diffusion Limited Aggregation

1. In this project, you will explore work on bacterial morphogenesis where diffusion of nutrients limits its growth. See the "Useful Links" Pattern Formation section.

Go to the directory (i.e. folder) hw4/dla. 

This code here, dla.py, simulates this. It also allows for a stickiness parameter. Calculate the fractal dimension of this object by modifying the attached code

1. Compute Rsq = square of the radius of gyration = (moment of inertia about center of mass)/(total mass)
2. Compute Rsq as a function of total mass.
3. Average this over many realization (add an extra for loop to enclose the existing one) in order to average.
4. Look at mass versus radius on a log-log plot. The fractal dimension is the slope of this line.

Now what happens when you change the stickiness parameter in the code? Does the fractal dimension change?

2. Modify dla.c so that instead of seeding the pattern with a point it is seeded with a line. Describe the kind of growth that you observe. Produce an image after the simulation has run for a while.

'Technical Note'

In the code given, random walkers are not released at infinity, but quite close to the cluster. A ring is drawn whose radius is large enough to contain the complete cluster and a particle is released at random from that ring. That is equivalent to letting it random walk from infinity. Why?

Modify that approach for the line case here. This will enormously speed up the code.

Here is an embedded C version of DLA using "weave" dla_c.py . This is much faster but harder to modify. But if you like C, then have fun playing with it!

3. Explain how the behavior of bacterial colonies can be similar to DLA.

• What parameter regime does the system need to be in to give similar fractal morphology?
• Find at least one other claim in the literature of where similar morphology is seen, and that attempts to link this to DLA. Do you find the claims convincing?
• Look into other reasons, mechanisms, or significance of bacterial colony patterns (fractal and non-fractal colony morphology).