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<!DOCTYPE html>
<html lang="en-US">
<!-- slides for the talk "A kaleidoscope of graph rewriting systems", Dec 4th 2019
author: Marius Buliga
last modified: 04.12.2019
//
-->
<head>
<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
<meta name="viewport" content="width=device-width, initial-scale=1">
<link rel="stylesheet" type="text/css" href="css/slides.css">
<title>Artificial physics</title>
</head>
<body onkeydown="plusSlides(1)">
<div class="slideshow-container">
<!-- slide 1 -->
<div class="mySlides fade">
<div class="numbertext"></div>
<div class="bigtext">
<p style="width:90%"><span style="color: #000000;">Artificial Physics for Artificial Chemistries </span> </p>
</div>
<div class="storytext">
<span style="color: #000000;">(1) artificial chemistries</span>
</div>
<div class="storytext"><span style="color: #000000;">(2) chemlambda </span>
</div>
<div class="storytext">
<span style="color: #000000;">(3) information content of the deviation from hamiltonian evolution </span>
</div>
<div class="storytext"><span style="color: #000000;">(4) chemlambda + physics </span>
</div>
</div>
<!-- slide 2 -->
<div class="mySlides fade">
<div class="numbertext"></div>
<div class="middletextleft"> </div>
<div class="middletextleft">
<a href="https://www.ncbi.nlm.nih.gov/pubmed/11712956" target="_blank">[Dittrich, P., Ziegler, J.,
Banzhaf, W. (2001)]</a> - an artificial chemistry is a triple (S,R,A):
</div>
<div class="middletextleft">
S - a class of <span style="color: #0066ff;">molecule types</span>
</div>
<div class="middletextleft">
R - a class of <span style="color: #ff0000;">chemical reactions</span>
</div>
<div class="middletextleft">
A - an algorithm for the application of the <span style="color: #ff0000;">chemical reactions</span> to
<span style="color: #0066ff;">a multiset of molecules</span>
</div>
<div class="middletext">
<img src="final/artchem2.png" style="width:400px">
</div>
</div>
<!-- slide 3 -->
<div class="mySlides fade">
<div class="numbertext"></div>
<div class="middletextleft"> </div>
<div class="middletextleft">
<a href="https://link.springer.com/chapter/10.1007/978-3-642-01284-6_14" target="_blank">[K. Tomita, H. Kurokawa,
S. Murata (2009)]</a> - a graph-rewrite automaton is a triple (S,R,A):
</div>
<div class="middletextleft">
S - a class of <span style="color: #0066ff;">graphs</span> for example trivalent graphs with colored nodes
</div>
<div class="middletextleft">
R - a class of <span style="color: #ff0000;">graph-rewrites</span>
</div>
<div class="middletextleft"> A - an algorithm for the application of the
<span style="color: #ff0000;">graph-rewrites</span> to <span style="color: #0066ff;">one graph</span>
</div>
<div class="middletext">
<img src="final/tomita.png" style="width:350px"> <img src="final/tomita2.png" style="width:350px">
</div>
</div>
<!-- slide 4 -->
<div class="mySlides fade">
<div class="numbertext"></div>
<div class="middletextleft"> </div>
<div class="middletextleft">
- an asynchronous graph-rewrite automaton is a triple (S,R,A):
</div>
<div class="middletextleft">
S - a class of <span style="color: #0066ff;">"molecules" (i.e. of graphs)</span>
</div>
<div class="middletextleft">
R - a class of <span style="color: #ff0000;">"chemical reactions" (i.e. graph-rewrite rules)</span>
</div>
<div class="middletextleft">
A - a <span style="color: #ff00ff;">random and local</span> algorithm for the application of
<span style="color: #ff0000;">graph-rewrites</span> to <span style="color: #0066ff;">one graph</span>
</div>
<div class="middletext">
<img src="final/tape_long_4653_2.gif" style="width:300px">
</div>
</div>
<!-- slide 5 -->
<div class="mySlides fade">
<div class="numbertext"></div>
<div class="middletextleft"> </div>
<div class="middletextleft">λ calculus <a href="https://www.jstor.org/stable/2371045" target="_blank">[A.
Church (1936)]</a> <span style="color: #ff0000;">is a term rewrite system</span>
</div>
<div class="middletextleft"> Terms:
<ul>
<li> variable: x, y, z, ... </li>
<li> term:
<ul>
<li>variable | </li>
<li>A B where A, B terms | </li>
<li> λx.A where x var, A term</li>
</ul>
</li>
</ul>
</div>
<div class="middletextleft"> Term rewrite rule:
<ul>
<li> β-reduction: (λx.A)B → A[x=B] </li>
</ul>
</div>
</div>
<!-- slide 6 -->
<div class="mySlides fade">
<div class="numbertext"></div>
<div class="middletextleft"> </div>
<div class="middletextleft">λ calculus <a href="https://www.jstor.org/stable/2371045" target="_blank">[A.
Church (1936)]</a> <span style="color: #ff0000;">is a term rewrite system</span>
</div>
<div class="middletextleft"> Term rewrite rule:
<ul>
<li> β-reduction: (λx.D)B → D[x=B] </li>
</ul>
</div>
<div class="middletextleft"> (1971, C.P. Wadsworth, <a href="http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.90.2386&rep=rep1&type=pdf">1990, J. Lamping</a>) <span style="color: red;">graph rewrite system</span>
</div>
<div class="middletext">
<img src="final/lamping.jpg" style="width:350px">
</div>
</div>
<!-- slide 7 -->
<div class="mySlides fade">
<div class="numbertext"></div>
<div class="middletextleft"> </div>
<div class="middletextleft">
<a href="https://www.pnas.org/content/pnas/91/2/757.full.pdf" target="_blank">[W. Fontana, L. W. Buss (1994)]</a>
- <span style="color: #ff0000;">ALCHEMY</span> = ALgorithmic Chemistry:
</div>
<div class="middletextleft">
S - a class of <span style="color: #0066ff;"> λ- terms in normal form</span>
</div>
<div class="middletextleft">
R - a class of <span style="color: #ff0000;">reductions</span>
<p> A + B → A + B + normal form of AB</p>
</div>
<div class="middletextleft">
A - algorithm of random application of a reaction to a random selection of terms
</div>
<div class="middletextleft">
<a href="https://www.sciencedirect.com/science/article/pii/030439759290185I" target="_blank">[G. Berry,
G. Boudol (1992)]</a>
- <span style="color: #ff0000;">CHAM</span> = Chemical Abstract Machine: a <span style="color: #0066ff;">programming
language</span> which uses molecules, solutions and transformation rules
</div>
</div>
<!-- slide 8 -->
<div class="mySlides fade">
<div class="numbertext"></div>
<div class="middletextleft"> </div>
<div class="middletextleft">
<a href="https://www.sciencedirect.com/science/article/pii/S0890540197926432" target="_blank">[Y. Lafont (1997)]</a>
<span style="color: #ff0000;">Interaction combinators</span>
</div>
<div class="middletextleft">
S - a class of <span style="color: #0066ff;">trivalent fatgraphs</span>
</div>
<div class="middletextleft">
R - a class of <span style="color: #ff0000;">graph rewrite rules</span>, without conflicts
<img src="final/lafont.png" style="width:500px">
</div>
<div class="middletextleft">
A - any algorithm will do for graphs which reduce in a finite number of steps</li>
</div>
</div>
<!-- slide 9 -->
<div class="mySlides fade">
<div class="numbertext"></div>
<div class="middletextleft"> </div>
<div class="middletextleft">
The Matrix: <span style="color: #0066ff;">what does it mean?</span><br><br>
"still he'd see <span style="color: #000000;">the matrix</span> in his sleep, bright
lattices <span style="color: #000000;">of logic unfolding</span> across that colorless void"
(William Gibson, Neuromancer)
</div>
<div class="middletextleft"> <span style="color: #ff0000;">versus</span>
</div>
<div class="middletextleft"> Blade Runner:
<span style="color: #0066ff;">is this alive?</span><br><br>
<img src="final/blade_runner_1.jpg" style="width:500px">
</div>
</div>
<!-- slide 10 -->
<div class="mySlides fade">
<div class="numbertext"></div>
<div class="middletextleft"> </div>
<div class="middletext">
Turing machines and λ-terms
</div>
<div class="bigtext">
<img src="final/test-105.gif" style="width:600px">
</div>
<div class="middletext">
<a href="http://chorasimilarity.github.io/chemlambda-gui/dynamic/turingchem.html">[explanation: Turing Machines, chemlambda style]</a>
</div>
</div>
<!-- slide 11 -->
<div class="mySlides fade">
<div class="numbertext"></div>
<div class="middletextleft"> </div>
<div class="middletextleft">
<a href="https://github.com/chorasimilarity/chemlambda-gui/blob/gh-pages/dynamic/README.md" target="_blank">[github repository]</a>
<a href="http://imar.ro/~mbuliga/chemlambda-v2.html" target="_blank">[explanations]</a> Chemlambda v2:
</div>
<div class="middletextleft">
S - a class of <span style="color: #0066ff;">trivalent fatgraphs<br><br>
<img src="final/nodes.jpg" style="width:500px">
</div>
</div>
<!-- slide 12 -->
<div class="mySlides fade">
<div class="numbertext"></div>
<div class="middletextleft"> </div>
<div class="middletextleft">
R - <span style="color: #ff0000;">two main families of graph rewrite rules</span>
</div>
<div class="middletext">
<img src="final/beta-fi-foe.jpg" style="width:300px"> <img src="final/fi-fo-foe.jpg" style="width:300px">
</div>
<div class="middletextleft">
which look like the IC rewrites
</div>
<div class="middletext">
<img src="final/deltadelta.png" style="width:200px"> <img src="final/gammadelta.png" style="width:200px">
</div>
</div>
<!-- slide 13 -->
<div class="mySlides fade">
<div class="numbertext"></div>
<div class="middletextleft"> </div>
<div class="middletextleft">
each IC node has only 1 active port, so no conflicts
</div>
<div class="middletextleft">
however chemlambda nodes have 2 active ports, leads to conflicts
</div>
<div class="middletext">
<img src="final/con-l-fo-foe-id-1.jpg" style="width:300px"> <img src="final/con-l-fo-foe-id-2.jpg" style="width:400px">
</div>
</div>
<!-- slide 14 -->
<div class="mySlides fade">
<div class="numbertext"></div>
<div class="middletextleft"> </div>
<div class="middletextleft">
R - <span style="color: #ff0000;">a COMB graph rewrite cycle</span> to eliminate the Arrow elements and loops <br><br>
<img src="final/comb.jpg" style="width:600px">
</div>
<div class="middletextleft">
R - and some <span style="color: #ff0000;">TERM rewrites</span> like the other IC rewrites <br><br>
<img src="final/a-t-fi-t.jpg" style="width:300px"> <img src="final/fo-t-foe-t.jpg" style="width:300px">
</div>
</div>
<!-- slide 15 -->
<div class="mySlides fade">
<div class="numbertext"></div>
<div class="middletextleft"> </div>
<div class="middletext">
Dodecahedron multiplication
</div>
<div class="bigtext" style="width:100%" >
<img src="final/dodecahedron.gif" style="width:500px">
</div>
</div>
<!-- slide 16 -->
<div class="mySlides fade">
<div class="numbertext"></div>
<div class="middletextleft"> </div>
<div class="middletext">
Tube pattern duplication
</div>
<div class="bigtext" style="width:100%">
<img src="final/spiral_boole_short.gif" style="width:500px">
</div>
</div>
<!-- slide 17 -->
<div class="mySlides fade">
<div class="numbertext"></div>
<div class="middletextleft"> </div>
<div class="middletext">
Tube pattern with Turing Machines, builts itself
</div>
<div class="bigtext" style="width:100%">
<img src="final/spiral_boole_bb_short.gif" style="width:500px">
</div>
</div>
<!-- slide 18 -->
<div class="mySlides fade">
<div class="numbertext"></div>
<div class="middletextleft"> </div>
<div class="middletext">
The factorial of 5: (a,b) to (a+1, ab)
</div>
<div class="bigtext" style="width:100%">
<img src="final/tubefact.gif" style="width:500px">
</div>
</div>
<!-- !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! -->
<!-- slide 19 -->
<div class="mySlides fade">
<div class="numbertext"></div>
<div class="middletextleft"> Properties:
</div>
<div class="middletextleft"> Turing universal: we can represent λ-terms and rewrites, or TM.<br>
<a href="http://chorasimilarity.github.io/chemlambda-gui/dynamic/expo_ackermann_2_2.html" target="_blank">
[Ackermann(2,2) simulation]</a>
<a href="http://chorasimilarity.github.io/chemlambda-gui/dynamic/demos.html" target="_blank">[Demos]</a>
<a href="http://chorasimilarity.github.io/chemlambda-gui/dynamic/molecular.html" target="_blank">[Molecular
computers (2015)]</a>
<a href="https://arxiv.org/abs/1811.04960" target="_blank">arXiv:1811.04960</a>
</div>
<div class="middletextleft">
gives many interesting graphs modified outside λ-calculus<br>
<img src="final/pred.gif" style="width:350px"> <img src="final/bigpred_train-opt.gif" style="width:350px">
</div>
<div class="middletextleft">
artificial life: a chemlambda quine is a graph deterministically periodic, evolving under the random algorithm.<br>
<a href="https://github.com/chorasimilarity/chemlambda-gui/tree/gh-pages/dynamic/mol" target="_blank">[Library
of molecules]</a>
<a href="https://doi.org/10.6084/m9.figshare.4747390.v1" target="_blank">[Collection of simulations]</a>
</div>
</div>
<!-- slide 20 -->
<div class="mySlides fade">
<div class="numbertext"></div>
<div class="middletextleft">The information content of the deviation from hamiltonian evolution, an extension of
Hamiltonian mechanics.
<a href="https://arxiv.org/abs/0810.1419" target="_blank">[Buliga (2009)]</a>
<a href="https://arxiv.org/abs/1807.10480" target="_blank">[(2018)]</a>
<a href="https://arxiv.org/abs/1902.04598" target="_blank">[(2019)]</a>
<a href="http://dx.doi.org/10.1177/1081286516629532" target="_blank">[Buliga, de Saxce (2017)]</a>
</div>
<div class="middletextleft"> aka "Hamiltonian inclusions with convex dissipation" or
"symplectic Brezis-Ekeland-Nayroles principle"
</div>
<div class="middletextleft">
define the deviation from hamiltonian evolution vector η
<p> <img src="final/dif-ham.png" style="width:300px"></p>
<p> <img src="final/eta-z.png" style="width:350px"></p>
</div>
<div class="middletextleft">
impose that the evolution minimizes the information content
<p> <img src="final/principle.png" style="width:350px"></p>
</div>
</div>
<!-- slide 21 -->
<div class="mySlides fade">
<div class="numbertext"></div>
<div class="middletextleft"> allows dissipation (a generalized Liouville theorem)
<p> <img src="final/disip-2.png" style="width:70%"></p>
</div>
</div>
<!-- slide 22 -->
<div class="mySlides fade">
<div class="numbertext"></div>
<div class="middletextleft">applies to: viscosity, plasticity, damage, fracture
</div>
<div class="middletextleft"> also to unilateral contact (and friction)
</div>
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<a href="https://doi.org/10.1007%2FBF01857727" target="_blank">[E. Fredkin, T. Toffoli (1982)]</a>
billiard ball computer
<p> <img src="final/Toffoli_BilliardBall.gif" style="width:80%"></p>
</div>
<div class="middletextleft"> Let M be the space (billiard), then the information content function is
<p> <img src="final/disip-3.png" style="width:80%"></p>
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<div class="middletextleft">stochastic version
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<p> <img src="final/disip-4.png" style="width:80%"></p>
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<div class="middletextleft">chemlambda+physics
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<div class="middletextleft">
A <a href="https://doi.org/10.6084/m9.figshare.5751318.v1" target="_blank">version of chemlambda</a>
is a billiard ball computer (with the physics as in the principle of minimal information content),
with some of the state variables over a pair of
<a href="https://en.wikipedia.org/wiki/Permutohedron" target="_blank">permutohedra</a>
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<center> <img src="final/permutohedron.png" style="width:350px"></center>
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<div class="middletextleft">chemlambda+physics
</div>
<div class="middletextleft">anatomy of nodes and edges:
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<center> <img src="final/node-ana.jpg" style="width:90%"></center>
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<div class="middletextleft">chemlambda+physics
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<div class="middletextleft">initial graph:
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<center> <img src="final/diagram1.jpg" style="width:90%"></center>
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<div class="middletextleft">chemlambda+physics
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<div class="middletextleft">a rewrite is a pair of permutations:
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<div class="middletextleft">
<center> <img src="final/diagram2.jpg" style="width:90%"></center>
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<div class="middletextleft">
<p> <a href="http://imar.ro/~mbuliga/beta.html" target="_blank">do the β like a boss</a> </p>
<p> <a href="http://imar.ro/~mbuliga/betaboss2.html" target="_blank">same with colored edges</a></p>
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<div class="middletextleft">chemlambda+physics
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<div class="middletextleft">we modify the hamiltonian of the force graph by using the state of the graph
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<div class="middletextleft">
we modify the information content and we use the stochastic version
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... and it works (announcement).
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CONCLUSION: is a game with a pair of permutohedron dices.
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<p style="width:90%"><span style="color: #000000;">Continue to my
<a href="https://mbuliga.github.io/" target="_blank">homepage</a></span> </p>
</div>
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