# Story telling

This program is under development.
is complete, remove the {{develop}} tag.

AutoAdv as an algorithm of automatic story telling.

It is based on an analogy with fractal landscape generation.

## Theory behind the AutoAdv algorithm

Let $\mathcal{E}$ be a set of at least two elements, two of them named:

• the initial element $I_\mathcal{E}$
• the terminal element $T_\mathcal{E}$

Let $\mathcal{P}(\mathcal{E})$ the set of subsets of $\mathcal{E}$.

Let $E\in\mathcal{P}(\mathcal{E})$, τE is called an timing of E when it's an application from E into $I\!\!R^+$ so that:

• if $I_\mathcal{E}\in E$, $\tau_E(I_\mathcal{E})<\min(\tau_E(x),\forall x\in E)$
• if $T_\mathcal{E}\in E$, $\tau_E(T_\mathcal{E})>\max(\tau_E(x),\forall x\in E)$

When $(X_1, X_2,\ldots,X_N)$ is a vector of N elements of $\mathcal{P}(\mathcal{E})$, and $(\tau_1, \tau_2, \ldots, \tau_N)$ a vector of N associated timings (i.e. $\forall 1\leq n\leq N, \tau_n$ is a timing of Xn), an augmentation of $\left((X_1, X_2,\ldots,X_N),(\tau_1, \tau_2, \ldots, \tau_N)\right)$ is $\left((Y_1, Y_2,\ldots,Y_{N+K}),(\tilde\tau_1, \tilde\tau_2, \ldots, \tilde\tau_N, \tau_{N+1},\ldots, \tau_{N+K}\right)$, where:

$\left\{\begin{matrix} \forall 1\leq n\leq N,& X_n \subset Y_n\\ \forall x\in X_n,& \tau_n(x)=\tilde\tau_n(x)\\ \forall y\in X_n\setminus Y_n,& \tilde\tau_n(y)>\max(\tau_{n}(x), \forall x\in X_{n})\\ \end{matrix}\right.$

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