this is for holding javascript data
Michael Retchin edited Math.tex
over 9 years ago
Commit id: fa398154dd6389d354d90c324db79e9bebddfb23
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After $n$ steps, the output of the function is defined as the sum of all previous movements. Thus, the position $S_{n}$ of the random walk after $n$ steps is described by the following equation:
\begin{equation}
S_{n} =
\sideset{}{}\sum_{j=1}^{n}e^i\theta j \sideset{}{}\sum_{j=1}^{n}e^{i\theta j}
\end{equation}
This equation is $1$-dimensional in that it only accounts for one axis of motion. To model tumors as $2$-dimensional, we used a random walk to model both axes of motion. As a result, the "tumors" were both randomly configured and contiguous.