We can program a computer to do anything. What if we had the same power over the molecules of our bodies?

This is a collection of experiments with chemlambda artificial chemistry, interaction combinators and lambda calculus. The goal is to explore the behaviour of such systems under the most simple random algorithms, implemented by local machines. This teaches us something about biological life, or if molecular computers inspired from graph reductions and lambda calculus are possible.

Experiments involve, among others, quine graphs. These are new proposals for artificial life. They can reproduce, die and they have a metabolism. Interesting lambda calculus computations, far more complex than simple circuits logic, can be done with local random rewrites algorithms. Lambda calculus, or more precisely graph rewrites systems inspired from it, can be taken as first principles when designing molecular computers. The simulations from the collection of animations show many examples of complex behaviour typical for living creatures, thus suggesting that real life, at molecular level, is the same kind of computation as (graphical versions of) lambda calculus.

This is a collection of experiments with chemlambda artificial chemistry, interaction combinators and lambda calculus. The goal is to explore the behaviour of such systems under the most simple random algorithms, implemented by local machines. This teaches us something about biological life, or if molecular computers inspired from graph reductions and lambda calculus are possible.

Experiments involve, among others, quine graphs. These are new proposals for artificial life. They can reproduce, die and they have a metabolism. Interesting lambda calculus computations, far more complex than simple circuits logic, can be done with local random rewrites algorithms. Lambda calculus, or more precisely graph rewrites systems inspired from it, can be taken as first principles when designing molecular computers. The simulations from the collection of animations show many examples of complex behaviour typical for living creatures, thus suggesting that real life, at molecular level, is the same kind of computation as (graphical versions of) lambda calculus.

- History of chemlambda: Graph rewrites, from emergent algebras to chemlambda or arXiv:2007.10288 [cs.LO] or (pdf) or (figshare)
- Artificial life properties of directed interaction combinators vs. chemlambda or arXiv:2005.06060 [cs.AI]
- (pdf) Artificial chemistry experiments with chemlambda, lambda calculus, interaction combinators or arXiv:2003.14332 [cs.AI]
- (working draft) Pure See
- chemSKI & chemλ, a chemlambda style purely local graph rewrite system for SKI combinator calculus.

- (js) chemski by mbuliga
- (js) quine graphs by mbuliga
- (js) chemlambda collection by chemlambda
- (js) chemlambda-editor by ishanpm
- (js) project hapax by mbuliga
- (haskell) chemlambda-hask by synergistics
- (python) chemlambda-py by 4lhc
- (awk,js) chemlambda-gui by chorasimilarity

- (slides and video) Emergent rewrites in knot theory and logic
- (video) Zipper logic revisited
- (slides, general audience) Chemlambda for the people
- (slides) A kaleidoscope of graph rewrite systems in topology, metric geometry and computer science
- (slides) Artificial physics for artificial chemistries
- (discussions) browse the (closed now) issues at chemlambda-gui

- directed interaction combinators vs. chemlambda chemistries, associated with arXiv:2005.06060:

- Alife properties of directed interaction combinators vs. chemlambda

- extra: 16 animations which supplement arXiv:2005.06060

- explore chemlambda and IC quine graphs (first version, with no article attached):

Interaction combinators and chemlambda quine graphs

- tools to find quine graphs and more examples:

How to test a quine

- molecules laboratory: input your own molecules

The quine lab - detailed explanation of the ouroboros quine, inspired from the lambda calculus predecessor term:

The Ouroboros - untyped lambda calculus terms can be reduced in chemlambda:

Lambda calculus to chemlambda parser - more than 250 animations from simulations, with comments and the possibility to run them in js:

Chemlambda collection of animations, salvaged from G+

Same collection with bigger pictures

Project hapax, aka "made of money" (not yet stable): a remake of chemlambda (and arbitrarily many other graph rewrite systems) as a conservative graph rewrite system,
with the help of tokens and permutation based automata. Articles and demos:

Zip Slip Smash is a rework of zipper logic, in development. More specifically, it combines tangle diagrams with zippers made with the help of directed interaction combinators.
It admits a denotational semantics of a pair of emergent algebras, one linear and the other commutative.

Available here, from the repository chemlambda-gui:

- Chemlambda vision: microbiome OS, autonomous computing molecules and biological digital converters
- Molecular computers with pdf version on (figshare) or arXiv:1811.04960 [cs.ET]
- Chemical concrete machine (figshare) or arXiv:1309.6914 [cs.FL]
- Zipper logic (figshare) or arXiv:1405.6095 [math.CO]
- Chemlambda strings (figshare)
- Turing machines, chemlambda style

Special thanks to the other authors of chemlambda repositories listed here. Their work greatly enhanced this project and also validated it. The discussions, see those listed here or in the issues of the other repositories, helped very much to clarify the subject.