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diff --git a/stochasticca.html b/stochasticca.html index 6f7bba9..f42ed01 100644 --- a/stochasticca.html +++ b/stochasticca.html @@ -7,17 +7,40 @@ <script src="https://ajax.googleapis.com/ajax/libs/jquery/1.12.4/jquery.min.js"></script> <meta charset="utf-8"> + <script type="text/x-mathjax-config"> + MathJax.Hub.Config({tex2jax: {inlineMath: [['$','$'], ['\\(','\\)']]}}); + </script> + <script type="text/javascript" src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script> <title>Stochastic Cellular Automata</title> </head> <body> <div id="navbar"></div> <script src="navbar.js"></script> <h2>Stochastic Cellular Automata</h2> + <p> + The parameters should consist of an odd number of numbers separated by commas. + </p> Parameters: <input type="text" value="-3, 3, -3" id="params"><br> Width: <input type="number" value="400" id="width"><br> Time: <input type="number" value="400" id="time"><br> <button id="display">Display</button><br> <script src="https://cdnjs.cloudflare.com/ajax/libs/p5.js/0.5.2/p5.js"></script> <script src="js/stochasticca.js"></script> + <div id="canvas"></div> + <p> + The probability of any cell being black is determined by the cells above it using this formula (where $\theta$ is a vector containing the parameters, + $t$ is the time passed (or row), and $i$ is the column): + $$L = \frac{||\theta||-1}{2}$$ + $$p(0, i) = 1$$ + $$\text{(when t > 0) } p(t, i) = \theta \cdot + \begin{bmatrix} + c(t-1, i-L)\\ + c(t-1, i-L+1)\\ + \vdots \\ + c(t-1, i+L) + \end{bmatrix}$$ + $$c(t, i) = \text{a number with a $p(t, i)$ probability of being 1}$$ + + </p> </body> </html> |