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@jemoka / Jemoka Knowledge Base / wiki/concepts/stepwise_evolution.md
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--- title: "Stepwise Evolution" type: concept related: [Vector Space, Dyson S Model Of Life, Matricies, Cell] source: https://www.jemoka.com/posts/kbhstepwise_evolution/ confidence: high status: active --- To put some math behind that very, extremely simple Dyson’s Model, we will declare a vector space \(K\) which encodes the possible set of states that our “cell” can be in. Now, declare a transition matrix \(M \in \mathcal{L}(K)\) which maps from one state to another. Finally, then, we can define a function \(P(k)\) for the \(k\) th state of our cell. That is, then: \begin{equation} P(k+1) = M P(k) \end{equation} (as the “next” state is simply \(M\) applied onto the previous state). Rolling that out, we have: \begin{equation} P(k) = M^{k} P(0) \end{equation}