Introduction

1. Introduction At the heart of the growth of a multi-cellular organism is the process of cellular division… … aka (in computing) self-replication

2. Von Neumann’s UC

3. Self-replicating CA • After von Neumann, nothing much happened for almost 30 years! • Why? Probably because the hardware wasn’t ready. • In 1984, Chris Langton designed Langton’s Loop

4. Von Neumann’s Constructor • The Pulser • Generation of a sequence of 0s and 1s • For u 0s and k 1s, the pulser has width 2 x k and height u + 2 (if there’s only a single 0 in the sequence, then the height is 2) Output (sequence) Pulser P Input

5. Von Neumann’s Constructor • Pulser P (101001) • k = 3, width = 2 x 3 = 6 • u = 3, height = 3 + 2 = 5

6. Von Neumann’s Constructor • Pulser P (101001) • k = 3, width = 2 x 3 = 6 • u = 3, height = 3 + 2 = 5

7. Langton’s Loop • Environment: 8 (?) states, 5 neighbours (von Neumann), rules designed by hand • Initial configuration: 94 active cells (vs. 200k+ in von Neumann’s Universal Constructor) • Replication occurs after 151 iterations

8. Langton’s Loop • Environment: 8 (?) states, 5 neighbours (von Neumann), rules designed by hand • Initial configuration: 94 active cells (vs. 200k+ in von Neumann’s Universal Constructor) • Replication occurs after 151 iterations

9. Langton’s Loop • Aim: studying self-replication as “Artificial Life” • Problem: does nothing but self-replicate

10. Langton’s Loop • After Langton, the loops were optimized • In one case (Perrier et al.) a Turing machine was added to the loop (but at a high cost)

11. Towards functional self-replication • Environment: 7+ states, 9 neighbours (Moore), rules designed by hand • Simple initial configuration, easily simulated

12. Towards functional self-replication • Can be extended by adding “applications” (the complexity depends on the task)

13. Self-replicating CA • After von Neumann, nothing much happened for almost 30 years! • Why? Probably because the hardware wasn’t ready. • In the 90’s, FPGAs changed the scenario

14. Self-replicating CA • Question: are the “standard” self-replicating loops well adapted to self-replication in FPGAs? Not really! Lots of empty space, huge lookup tables, and infinite grids! • New algorithms are needed

15. The Tom Thumb algorithm • In an FPGA, self-replication = copy of the configuration (seen as a state) • Need algorithms that can evolve in an FPGA environment – look at von Neumann!

16. The Tom Thumb algorithm Simple(st) example: Assume a configuration (shift) register of 4x4 bits

17. The Tom Thumb algorithm - States Data information

18. The Tom Thumb algorithm - States Data information

19. The Tom Thumb algorithm - States Flag data

20. The Tom Thumb algorithm - States Flag data

21. The Tom Thumb algorithm - Rules • Instead of a look-up table, the rules are defined by the motion of data and signals

22. The Tom Thumb algorithm - Rules • Instead of a look-up table, the rules are defined by the motion of data and signals

23. The Tom Thumb algorithm Note: the genome must be injected twice

24. The Tom Thumb algorithm

25. The Tom Thumb algorithm Loop of 2x4 molecules

26. The Tom Thumb algorithm Loop of 4x4 molecules

27. Basic cell made of 12 x 6 = 72 molecules The Tom Thumb algorithm - Example Original specifications

28. The Tom Thumb algorithm - Example Genome made of 144 characters

31. Ontogenetic hardware • Ok, so the Tom Thumb algorithm can self-replicate an arbitrary structure within an FPGA • But what kindof structures is it interesting to self-replicate • And why would you want to do it anyway?