Following on from the last post I’ve been digging a little deeper to see how these tree-like branchy things behave.

The variable I chose to look at was the fertility of the occupied squares, either:

  • All occupied squares can start new growth regardless of their age.

or

  • Only squares that have been occupied for fewer than N time steps can start new growth.

Call the cut-off age the fertility.

I set the fertility to 30 time steps and ran the simulation for 1000 time steps 1000 times. Here’s the results:

 

to30-1000steps.png

How does this compare to cells that are fertile forever?

 

Histogram.png

So ‘fertile forever’ is not what we want. Here’s a video of a branch that’s fertile forever:

And now look at one with the fertility is set to 30:

Branches where every cell can spawn new growth seem to spend too much time adding cells to their centre which doesn’t increase their fitness much because they open up fewer neighbouring squares.

We see more branching in the plant whose cells are only fertile up to 30 time steps which is really interesting. It branches more because new growth tends to be at its edges.

I repeated the histogram plots for fitnesses of 10 and 20, too. Here they are on the same  graph:multiHistogram.png

 

It’s striking how inconsistently 10 behaves!

There’s so much to play with in these models, next time I’d like to look at changing the probability function the branches use to decide whether to grow or not. Recall at the moment I’m using an expit function:

 

plot

Next time I’ll see what happens if I mess around with this. Perhaps a step function? Or one of these?

expits.png

We’ll see.