# OrganiComplex
Interactive complex-valued cellular automaton on 2D and 3D grids in search of that stuff — emergence, open-endedness, organicity etc. Uses [SDL2](https://www.libsdl.org/).
Accompanies the "paper" (rather draft) with videos called [“OrganiComplex: probes into complex-valued cellular automata with topologically universal update rules using certain reflections”](https://sunkware.org/organicomplex/index.html), where there is more thorough consideration of structures that appear in one such automaton and their dependence on its parameters.
## Look
## Deployment
Get source, build, and copy the binary into the unpacked root dir taken from the paper above (link below Abstract). Run the binary.
`ESC` brings main menu, where `Help` lists controls.
## Recipe
Basically, you take cellular automaton (CA) from [J.H. Conway's "Game of Life"](https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life) and
**1)** change set of states of each cell from $\{0, 1\}$ to complex plane ℂ,
**2)** modify update rule to take complexification into account, using non-linear mappings, conjugation etc., and some normalisation so that states remain bounded in some zero-centered, e.g. unit, disk and do not diverge to $\infty$,
**3)** and slightly adjust neighbourhood to include not only adjacent neighbours, but their neighbours as well, then maybe theirs and so on.
Voilà, — *complex-valued* CA (ℂCA). And if the combination of 1-2-3 choices is "right", you will observe some "interesting" behaviour... otherwise, you will not observe it... well, hasn't this statement been a tautology all along, since we *define* "right" as "leading to interesting behaviour", right?
## FilamentiComplex
In OrganiComplex, the default 1-2-3 combination — and the automaton it specifies — develops certain filamentiferous (hypha-, worm-, snake-like) structures, somewhat organic in their behaviour, so we call this automaton as the title of this section reads (also, FℂCA):
$$s_j' = M \bigl( 1 - \min \{ 1, |S_j'| \} \bigr) S_j'$$
$$S_j' = s_j + \overline{\sum\limits_{k \in \mathcal{N}(j)} s_k^2 } + \zeta$$
where
• $s_j$ and $s_j'$ are current and next state of $j$-th cell, respectively,
• $\overline{z}$, as usual, denotes complex conjugation of $z$, $\overline{a + bi} = a - bi$,
• $\mathcal{N}(j)$ is the $5 \times 5$ neighbourhood of $j$-th cell with this cell at its centre,
• $\zeta$ is a random isotropic "noise" with modulus bounded by $R$ (or absent, $R = 0$),
• $M > 0$ is the scaling multiplier with $M = 0.53 \pm 0.02$ being "optimal".
Indeed, there should be other combinations ensuring "organicity", even better at it than FℂCA... for you to find.
## Non-QM/ANN-ness
The majority of researches in this area deals with ℂCA based either on Quantum Mechanics (QM) or on Artificial Neural Networks (ANN); there is an entire field called ["Quantum Cellular Automata"](https://en.wikipedia.org/wiki/Quantum_cellular_automaton) (QCA), rich in authors, papers, and books.
The default update rule in OrganiComplex (that is, FilamentiComplex) is *not* QM- or ANN-based, at least to our knowledge, explicitly... in fact, there is no nature-grounded motivation for this particular kind of rules, beside their computational speed and "organic-like" behaviour they provide... for some reason.
You are welcome to switch back to QM and/or ANN. See also References in the "paper".
## Customisation
See `Field::update()` in `src/play/automaton/field.rs`. There are some commented alternatives to FℂCA already.
For instance, change `nextamph += neigh_cell.amphunc` to `nextamph -= neigh_cell.amphunc`.
## Optimisation warning
Build with **release** profile, because with debug one it works much (20+ times) slower.
## Cf.
[github.com/Chakazul/Lenia](https://github.com/Chakazul/Lenia)
[github.com/GollyGang/ready](https://github.com/GollyGang/ready)
[github.com/MicahBrun/Continuous-Complex-Valued-Cellular-Automata](https://github.com/MicahBrun/Continuous-Complex-Valued-Cellular-Automata)
[github.com/mochiFnana/cellular-automata-with-julia](https://github.com/mochiFnana/cellular-automata-with-julia)