deletions | additions       diff --git a/Tumor Generation.tex b/Tumor Generation.tex  index 1ef09a6..3666cf6 100644  --- a/Tumor Generation.tex  +++ b/Tumor Generation.tex 
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\subsection{Tumor generation}   \hspace{20 mm}Each mm}By default each cell in the lattice is classified as normal tissue. Each  tumor was then  modeled as a self-avoiding walk (SAW). A SAW is a random walk path which does not visit the same site more than once. Mathematically, for a SAW of length $N$ in a $2$-dimensional lattice ${\Bbb Z}^2$, starting at point $x$, is defined as a path \begin{equation}  ω=(ω_0, ω_1, ..., ω_n)  \end{equation}  It follows that $ω_d ∈ {\Bbb Z}^2$, $ω_0=x$, $|ω_d − ω_{d−1}| = 1$, $d = 1, 2, . . . , n$, $ω_c \neq ω_d$ for $c \neq d$, and $0 ≤ c < d ≤ n$. In other words, no new step (each of which is a length of $1$ in a discrete direction in the real plane) can occur such that the path coincides with itself in two distinct events. Put in context, this means that two tumorous cells cannot occupy the same space.  A program was then constructed in the Python programming language where a pseudorandom integer $e$ (100 ≤ $e$ ≤ 9,000) was generated. A SAW was then continuously generated, where each new step filled in reclassified  exactly $1$ cell as tumor, untilthe  $e$ cells of the lattice were filled with tumor. Tumors were therefore generated to have both a random size and shape. The following pseudocode describes this algorithm programmatically: