A visual introduction and software to 
You just have to know that time elapses upward.
The pictures are orbits or spacetime diagrams of a special kind of dynamical systems called signal machines. In a onedimensional space, dimensionless points move in a uniform way, when the collide, they are replaced according to rules.
This dynamics system was devised for my Habilitation à Diriger des Recherches (DurandLose, 2003) and is investigated since.
In 2014, these researches have been presented in the french newsstand journal Pour la Sciences (Delahaye, 2014, in French).
The existing signals are instances of metasignals. The metasignal (speed) and rules in the first picture on the left are:
 

This signal machine is used to generate the picture on the left.
From a simple accumulation to the accumulation on a Cantor set
This is one way to achieve Turinguniversality, 2counter automaton are easy to implement, but their computing time has an exponential slowdown.
The side signals generates the boundary
So that it is possible to be Turing universal with only 13 metasignals (DurandLose, 2011a).
Cyclic tag systems were proven Turinguniversal and used to prove the universality of CA rule 110 ((Cook, 2004))
One iteration of the CTS is shown as well as a full computation.
So that it is contained in a bounded part!
It uses above constructions infinitely iterated.
Empty structure on the left and with a diagram embedded inside on the right
Accumulation arise naturally as fractal are generated.
They can be used to do analog computation in the understanding of computable analysis (Weihrauch, 2000,DurandLose, 2011b) and also of the semialgebraic approach of Blum, Shub and Smale (Blum et al., 1989,DurandLose, 2007,DurandLose, 2008).
As displayed, 4 speeds are enough to generate an accumulation. With 2 speeds (regardless of the number of metasignals) it is impossible to generate any.
What about 3 speeds? the answer is interesting and involves Euclid’s algorithm!
Which means as unpredictable as whether a program computes a nontotal function (one jump higher than the halting problem) (DurandLose, 2006)
This figures solves the satisfaction problem of the formula (x_{1}∨¬ x_{2})∧ x_{3}. Any SAT instance can be solves in such a way (Duchier et al., 2010).
The model from Jacopini and Sontacchi (Jacopini and Sontacchi, 1990) generates/interprets finite polyhedron as spacetime diagrams and computations.
The model from Huckenbeck (Huckenbeck, 1989,Huckenbeck, 1991) uses compass and ruler as primitives.
These models are presented in (DurandLose, 2016) (under press) or (Becker and DurandLose, 2015) (in French).
A simulator and dedicated languages has been developed to implement the various constructions and generate illustrations. This is a prototype used for research not a fully developed, tested and commented piece of software.
Although it is possible to encode everything in java (this was done for a long time), I developed a language not to made things simple and readable.
/* To launch this example work java jar agc_2_0.jar example.agc */ use AGC ; // To load AGC librairy signal_machine := create_signal_machine { // create a signal machine // Define metasignals (inside the machine) a := add_meta_signal ( "==" , 3 ) { color := Red ; } ; b := add_meta_signal ( "<<" , 3 ) ; // Define a collision rule (inside the machine) [ a , b ] > [ b ] ; // Create a configuration (inside the machine) c := create_configuration { a @ 7 ; // Add a signal at a position a @ 10 ; a @ 15 ; a @ 1 ; "<<" @ 6/3 ; }; // Create a run r := c.run () ; // advance to next collision r.step () ; // advance by 2 collisions r.step ( 2 ) ; // Create a pdf output of the run r.export ( "PDF" , "./out1.pdf" ) ; } ;
It can be executed with the following runnable jar: DOWNLOAD. It needs java 11 or higher.
java jar agc_2_0.jar <file.agc>
Sorry it does not come with more explanation, but the example should provide enough clues for a basic use. There is nothing special about this language and syntax and semantics are straightforward. This is a full Turingpowerful language along with loop, conditional execution, function definitionâ€¦
I started writing some documentation for the specific signal machine instructions.
This comes as is with no warranty of any kind.
Feedback, comments, bug reports are welcomed.
This document was translated from L^{A}T_{E}X by H^{E}V^{E}A.