 # Blairs in a Forest: Oh k

Blairs in a forest are so cool, that any humans they touch turn into Blairs in a forest. I created a simulation to show this phenomenon. We see that the Blairs grow with logistic growth thanks to the graph that appears in the simulation, with t on the x axis, and current number of Blairs on the y. This is what it looked like for one of the simulations.

The simulation was changed several times, from 20 total possible Blairs, to 40 total possible Blairs, to 80 total possible Blairs, to almost 600 total possible Blairs and 80 total possible Blairs in a smaller space.

After doing 4 trials with all these versions (except the 600 Blair version) I put all the numbers on a spreadsheet.

Then, using the equation dy/dt = ky(M-y) and turning that equation into y/M-y=e^Mtk*e^c I can and did use these equations to find the k values at each point, the average k values for each trial, and the average k value for each version. These are my findings:

The larger the population, the faster the simulation ends, and the k value gets smaller.

In a smaller environment, the trial ends faster, but the k value gets bigger.

So now in the next Apoca-Blair, you know what changes the k value of his logistic growth.