Turing Trains

 

computational train track layouts

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Train and Track

We've all at some time enjoyed playing with a model train layout. Straight and curved track pieces are joined together to create loops and sidings. The train is set running and enters a predetermined route, obediently following the track we've laid. Without any dead-ends, it will run around the layout forever.

Points switch the train between different sections of track. They alter the trains course and choose which route it traverses. The points act like binary switches, with two positions, 0 or 1.

This raises a few questions which these pages will answer:

1/ What is the best method for designing computational layouts? Computer programs carefully avoid complex tangles of code because it makes fault finding (debugging) tricky. Likewise, we want to avoid great layouts of tangled spaghetti.

We'll solve this by using sublayouts or subroutines.

2/ Can layouts be built that actually do some kind of logical computation? They at least need to be able to count and add.

We'll construct a few compact, self contained layouts, like an Input Follower or a Random Number Generator.

3/ Can we use layouts to construct some kind of general train track computer, capable of programmable logical computation? We will need to employ a modular approach to keep the design manageable.

We'll build and program a Train Track Computer.

4/ Can we use these design techniques to create more interesting layouts? For instance, 'display' type layouts where the train completes long uninterrupted runs without human intervention.

Some 'maximum run' designs are explored as Auto Switching Layouts.

Alan Turing

Alan Turing, the famous British computer scientist helped develop a theoretical model for a general purpose computer. To work, it assumes layouts can be infinite in size, so not a practical solution to many computational train track problems.

The layouts on these pages can be constructed with real pieces of track. Indeed some have been built with Duplo track sections. However, some of the more complex designs may need quite a lot of track, and correspondingly large floor area.

Alan Turing
Alan Turing

Chalcraft and Greene

In their paper Train Sets, Chalcraft and Greene describe a method of building a Turing machine using train track points and sections of track. Their paper sets out many key terms and definitions which I've followed on these pages.

So to begin, lets get a train and lay some track...

Train

A single train engine will run along the track computing as it goes. The train only moves forwards, it never reverses.

The train is non-intelligent. It cannot store data or information. It cannot mark or count the tracks or somehow work out its position. It is a simple source of power, driving relentlessly forward.

If the train returns to its start siding, it halts as it hits the buffers and the calculation is complete.

Track

There are two basic types of track, straight and curved:

Straight straight straight including cross-overs cross over

There is only one train, so bridges are not needed as there cannot be a collision between trains. Layouts with no bridges (only cross-overs) are called 'planar'.

Curved curve curve curve curve and (rarely used) dual curves curve curve

So far, we can create a simple loop:

Simple Loop
simple loop
Click layout to pause/run train. Click start to reset train.

Not much computing happening here. To do more, we need to be able to interact with the layout using points, Lazy and Sprung, which we'll look at next.

Duplo

Layouts on these web pages are depicted with a square track geometry. The sharp 90 degree curves are unrealistic for a train track layout, but it does produce very compact designs. Duplo layouts use a hexagonal geometry. (See Duplo pages).

Of course, both geometries, along with other train track standards, are topologically equivalent. This means any of the layouts can be built using any track system, although some will require more room than others.

Turing Trains | cr31.co.uk | 2017

 

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