# Complex Tips

On one side of the perspective your analytic object, a model, a
design, a scheme pretending to picture your subject. A 2^{nd} side of
perspective: complexity constraint, meaningful pathways, irreversibilities,
strange things, anything that shorten your perspective, constraint and limit
your proceedings. A 3^{rd} direction of perspective, scientific
reasons, consistency, efforts, what you know, but also what you should know
since information supports. A 4^{th} direction of perspective that
justify your criteria, legitimacy (but not guarantee goodness), make your acts
humane, establish your responsibilities, and so on...

Now there are things, forms, patterns, more rational "strange" behaviors that can inspire in different ways. Trajectories that are more realist. Included in residual of models, things that have been sided, from where can emerge and express complexity of effects. Pieces for modelling or include in deterministic or probabilistic models some precautions to prepare you, not to be too surprised. Many complex pieces have been discussed in litterature. Many have turned models of effects and simulated. Some have catalogue. Few have been practically included in applications. Some have derived from epistemological insights since formal sciences. Often they are somehow incorporated in different ways for simulations. Just here to introduce to some of them, not a systemic catalogue. We use them intuitivelly as patterns, to inspire motions, and so on ...

## Principles

"Axiomatically-like"you need to mind that real numbers algebra are not complete. Mind Godel and think that perfect algebra cannot in absolute self-made its truth. Step to decidability of program and see that all complex are not, with Church. Care that if mathematics is with logics the perfect science of demonstration; many problems are not mathematically solvable (read Chaitin). Remenber Clausius's principle of entropy be a consistent "virtual", a trend and an information. Seek Prigogine for irreversible thermodynamic systems.

"Lemmatically-like" you should care too:

- Abel's impossibility to solve algebraic real equations of 5 or more degree, with rational (Nature's mathematicity?)
- Scientific system of Carnap was not generally true but Hintikka (?) shows it to have some truth (requalify),
- Automata, completeness and iteration with Post and Turing (up to characteristics limits of steps?),
- See Prigogine and Atlan about that we are dissipative dynamic systems and not fixed for ever (ghosts?),
- Theory of Games since von Neuman, but think that plasticity or flexibility maintain goals by changing rules and varying strategies (transient rules),
- Theory of information, with Shannon, but mind slightly more complicated than in linear communication,
- Escher's forms are essential to visual mind,
- Fuzzy logics as the method of the option "I do not know", after Zadeh up to Smarandach's neutrosophic logic (it seems?)
- Morphogenesis of structures deduced or induced, since cristal ice to embryology: sources on how shapes configurate (remind Thom with Wolfram).

## Time's Tips (information tips)

### Ergodic or Brownian Motion

Physical spontaneous motion of non determined particle, impredictable in their elementary directio, essential to probability ant its model of urn's randomness sample. Historically Einstein and Poincaré.

### Markov Chains and Celular Automata

Motions making any step, not related to previous, so very related to previous, while more concerning time. Cellular automata being in a networks, not fully determined, not fully undertermined, somehow unruled but providing patterns, with simple motion that could be macroscopically very complicated, like percolating. Between Markov and Wolfram

### Explosive non linearity

Exponential increase being a limit, non linearity often showing catastrophic locally unexpected development, very closely looking like close trajectory, and very sensible to initial condition, brutally diverging, creating like "butterfly" catastrophic effects (pushing storms). Intuitivelly we think in reality out computer simulations that such sort of behaviors and expansion need some "environmental help" say like dominos' disposal.

## 2D Tips

Curious or strange effects are often not related to perfect integer dimension that is not exactly 1 or 2 or 3. But some are often seen at 2D (2 dimensions: plan), patterns and so on. Also many phenomena happen in such devices, experimental or real as in plains, sand dunes, slopes, snow or mudflows, etc.

### Cobordism and bifurcations

Topological ground of mathematical bifurcations, where a given interval of the graph of a function, on one axis interval a function has more than one value (no unique solution) but various and/or there are different derivates at one same point. A problem since differential calculus use derivation for calculating or examine these points. They generally come by folding(s) of plane supporting the graph of the function, in another cut of plane. Historically it has grounded theory of catastrophs. There is a a catalogue of basic bifurcations (pitchfork and so on). Thom started it, Arnold achieved it.

### Black Box

From the systemic and cybernetics: some box or place of function or system where nothing is known about which trajectory or functional behavior are in there. With cybernetics (starting with Wiener) it has been infered that control, servo-mechanism could be nevertheless established, controlling input and output: coupling them. Figurativelly there are plenty of things we ignore, set some attitude toward and determine or act, or use; depiste not being sure of the reason why. Only that we have method especially probabilistic ones, that inform us what works or not works but uncertainly. The aim is preciselly to be conscious of what sort of truth or evidence we use and how to manage in our artistic epistemology. Many users of applied sciences often ignore that.

### Constructal or Fractal

Emerging new properties and things from non integer dimension up (at the reverse of fractal), spontaneous generation or only because specifying reveals local properties, within safer or smoother conditions of expression. Diversity created within a range of possibilities. Investigate Bejan.

Self similar patterns obtained by cutting integer dimension. Pattern looks like the same at micro and macroscale, like if complex system could be not so "complicated", able, this procedure to fill quite looking-like real landscapes (and artistic forms). With grounds back to the thirties of past century then Mandelbrot, during the seventies.

### Replicators

Local micro undetermined, while macro-providing looking like patterns and structures. See for example Nicolis and Prigogine explanations on Belusov-Zabotinski's chemical reactions. Mind that you have sort of ghost procuring transformations.

### Percolations

In a column, or a flow or a surface, as diffusing molecules or particles in media, like markov diffusing object, on dunes' sand, the rolling stones on the slope, or on the river bed. Inability to describe exact trajectories, why ones exactly the same will get out first and others at different moments.

### Ying & Yan

See our use of Yin & Yang as a principle of primary model of complexity.

## 3D Tips

### White Box

Where too many things do not let you see or study any onin particular and picture it as an average. You get no contrast, smashed perspective. May be to look at together with quantic logic. Our general fate reducing everything just produce too much artificial and wrong (?) complexity. For example if you pretend the more simple expression of formal science having to rule: if you make that since a central office it can only mean that, in the field, legitimate actors will be disqualified and even more competent will be taken for fool or for dumb.

### Strange Attractors

3D partterns with locally unpredictable catastrophic changes. But with a pattern when at higher perspective, like clouds of trajectories with different radii, switching from one plane to another, and getting back; long after, close to original pattern. a property of chaos. To mind like if a complex irreducible pattern could structure while not showing at microlevel any of this structure or some unexpect on Poincaré's little cards. See Lorent'z curves.

### Implosive non linearity

Reducing or fragmenting, may make you loose your unity, observing when it is about your sustainability, as minimum as you can, or break your maximum complexity unit turning you into pieces or inducing apoptosis. A sort of dramatic suicide of living cells for the sake of metamorphosis. Out the biological analogy, to imagine when relative meso level vanish or reduce dramatically and macro may be, but not necessarilly. Delivered meso pieces may qualify for other and/or should face transformations for release. Mathematical forms as slow down or scale down, may perhaps, be studied on negative branch of logarithm expression.

### Ying & Yan magic ball

Mind our Ying & Yan plane model if a 3D ball. The tip of the claw (in the plane picture) turns a circle (like an oligopolic assembly of the "Round Table's Knights"?). May be put that "inside" some Klein's bottle.

## Corner of the Alchemist

Consider the undecidability, uncompleteness, width of correct demosntrations and probability, that is also contrary probability and non determinism. It is still not well clear if simulating complexity (simulating somehow determine) can have enough with some simple complication introduced in a deterministic model, or if all the different pictures already existing about complexities could have some interest. Yes some major contributors could have said complexity was not very useful (read Ruelle). Others have shown that some chaotic systems can after all be regulated (synchronized, etc.). After this point of usefulness of variety in "determined" simulations of underterminism, will come the turn of the difficulty to mind which pattern could be used and how to introduced them in models.

With a pragmatic view on: see real parts they do not look like simple, add subjective criteria, your reasons and closure will come for your rights and responsibilities. Meanwhile, with an open mind, forms, patterns and trajectories seems to us very intuitivelly interesting, for managing a bit more properly uncertainties and certainties.

### Butterfly' Dominos

Mimic, may be good or wrong, right or bad but that is an engine. "Once upon a time there was a butterfly, and the sweet beating of its wings made a hurricane". May be not so impossible, it some revealed after appropriate spatial disposition of winds, obstacles, free spaces or dominos' field could have been catch by the butterfly's flight. After climatic simulations, Lorentz discovered the reliable determinist unpredictability of climate further them few weeks. Unwiselly this did not prevented to dedicate so much talent to satisfy useless curiosity, instead supporting these good mathematicians for dedicating themselves to help communities quantifications: from public writer to public calculator; part time job. Grothendiek should have been seen better.

### Rubick's Cube

Something fascinating but try also the game to get from one complex pattern to another. Not just get to the reduction of one lone color face: all wise unpurifiers of the World, unity in the ergodic Populism and we will be saved!

Try also the shorter way to complete disorganized face, as a way to study mixture, dispersion, economic pathways to mixed reconfigurations. These are may be more interesting than trying to be the first and the only champion to reach something which is after all opposite of the games of reality: confuse and surprise us.

### Ying & Yan Spiral

Mind the previous with scaling and sort of mixing and confusing dynamics. Multiple levels of scale and in which extend pieces with non regular, non rigid motions may look like.