We nned to plot the spatial correlation function \(C(r)\) for \(r\in [0, R]\). where \(R\) is potentially the max distance between tiles.

$$ C(r) = \frac{1}{c_0} \frac{\sum_{i} {\gamma_i} \delta(r-r_{i})}{\sum_{i} \delta(r-r_{i})} $$

where

$$ \delta(r) = \frac{1}{a\sqrt{\pi}}e^{-(x/a)^2} $$ for some small value of $a$ (say a=0.01)

and \( c_0\) is chosen such that \(C(r=0) = 1\)

and \(r_{i}\) is the distance between tiles

Criticality Reference

Are Biological Systems Poised at Criticality?