CULET: a robotic Turing machine

CULET is a robot capable of emulate the behaviour of any 2-symbol Turing machine. It is built with Cubelets extended with Lego bricks [1].

This page contains some examples of Turing machines implemented in CULET, a list of the materials for build CULET, links to the code of the reprogrammed cubes and some photographs of CULET.

Some examples

A machine that emulates the evolution of Rule 110 elementary celular automata. This machine is proved to be universal [Coo04].

A machine that duplicates the number of ones at the beginning of the execution. This machine is described in [Ren16].

List of materials

Cubelets

• 2 batteries

• 1 bluetooth

• 2 distance sensors

• 2 drives

• 1 flashlight

• 1 passive

• 1 rotate

• 3 brick adapters

Lego bricks

• 3 angle plates 1X2 / 2X2

• 2 bricks 2X2

• 2 bricks 2X4

• 2 cross axle 10M

• 4 bushs for cross axle

• 4 plates 1X2 (rocking)

• 4 rocker bearings 1X2

• 1 plate 2x12

• 3 plate 2x16

• 1 plate 2x10

• 4 plate 2x2

• 4 plates 2x4 [2]

• 6 plates 2x6 [2]

• 4 technic brick 1X2, Ø4.9

• 4 Tires 30 x 10.5 with Ridges Inside

• 4 Wheel Rim 10 x 17.4 with 4 Studs and Technic Peghole

• 4 Brick 2 x 4 with Pins

• 4 Wheel With 43.2 x 28 Balloon Tyre

• 225 bricks 2X4

• 13 plates 4x10

Code of the reprogrammed Cubelets

The main program run in the rotator cube. Here is the C++ program for producing the code that must be programmed in this cube. The output depends on the Turing Machine that is going to be implemented: here is the input for producing the ECA rule 110 emulator, and here is the one for the duplicator machine. The C programs produced, respectively, are this and this.

Additionally, the motors and the flashlight needs too custom programs: this is the one of the motors, and this the one of the flashlight.

Some photographs

The idea of this section is to show a closer look of some of the details of CULET.

Previous model

One of the early models of CULET was like this logic gates: the idea was use the flashlights and the distance sensors as cells.

CULET in different mediums

• A participation in the 2019 edition of the ICAROB: the International Conference on Artificial Life and Robotics, in Beppu, Oita, Japan. GS1-3.

• A presentation in the event 60 years of computing in Mexico and the influence of Harold V. McIntosh, in ESCOM-IPN, Mexico.

• A presentation in the first seminar of artificial life and robotics, in ESCOM-IPN , Mexico.

• An entry in the Engineering our Future blog, at UWE.

Credits

This work is a collaborative project between the Artificial Life Robotics Lab (ALIROB), at the National Polytechnic Institute, in Mexico, and the Unconventional Computing Lab (UCL), at the University of the West of England.

• Ricardo Q. Figueroa, ALIROB.

• Daniel A. Zamorano, ALIROB.

• Genaro J. Martínez, ALIROB, UCL.

• Andrew Adamazky, UCL.

References

• [Ren16] Paul W. Rendell. Turing Machine Universality of the Game of Life. Springer, 2016. https://www.springer.com

• [Coo04] Matthew Cook. Universality in Elementary Cellular Automata. In: Complex Systems 15.1 (2004). https://www.complex-systems.com

Footnotes

• [1] Cubelets and Lego are register trademarks; here are used with non-comercial purpouses.

• [2] Two of this bricks must be of a bright color.

Copyright © 2018 ALIROB