No matter how much I play with these growth models I can’t shake the feeling that I’m just scratching the surface.

Here’s what happens when we change our plant’s growing preferences.

So far the algorithm has been

  1. Identify a potential new square to occupy
  2. calculate how this would change your fitness value
  3. decide if you should occupy the new square.

recall that a plant’s fitness is defined as latex-image-1

and that we have been using an expit curve as our transition probability function:

 

plot

 

See the previous post for the python code.

For this curve new growth that doesn’t improve the plant’s fitness is accepted 50% of the time. Growth that lowers or raises the fitness by a given amount is favoured/avoided equally strongly.

But we could have all kinds of different shapes. Let’s see what happens if the plant is really laid back and is more accepting of small decreases in fitness. i.e the curve is shifted left:

plot.png

Now our growth looks like this

What’s the word? It looks more clumpy? That’s what you get when the plant casually accepts new growth even if it doesn’t increase fitness. Now let’s do the other direction with the expit function shifted right by 5:

Now we have a plant which is far more stingy. It only adds new growth that is particularly beneficial to its fitness, hence the preference for diagonals!