Benedict Irwin edited Introduction.tex  about 10 years ago

Commit id: 1351ba1962575edbfb61433a370abd6bc91abd26

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The cellular automation like data map was first discovered when analysing a program investigating bound states in a rectangular 2D box. States for a box of dimension $(x,y)$ which were not bound were highlighted on an $(x,y)$ pixel map and a rich structure akin to a diffraction pattern is witnessed. Visual analysis found a subpattern which gave information about the primes when interpreted in the correct method.  The generator for the prime data map is a simple function. For some $n $n,m  \in \mathbb{Z}$, let \begin{equation} x_0 = (2n-1) \\  y_0 = 1 \\  dx = (2n-1) \\  dy = 1 \\  x_n x_m  \to x_{n-1} x_{m-1}  +dx \\ y_n y_m  \to y_{n-1} +dy y_{m-1} +dy.  \end{equation} If this is made  for allof the  $n$ limited (limited  by the maximum number you wish to check.  If at each $(x,y)$ in check) and  the sequence $(x_m,y_m)$ are plotted as  aposition is  filled with value 1, then pixel (value of 1)  the pattern map is created as seen  in Figure 1 occurs. 1.  This pattern has an interesting interpretation. If all positive integers $m$ sit in the coordinate $(m,m)$ as the strong, bottom line, then thier divisors are diagonally positioned upwards. Hence if there is no filled position between the coordinate $(m,m)$ and $(2m-1,1)$ then that number $m$ is prime.