## Game of Life in Scratch

A few days ago I asked for volunteers to read a book I was writing on programming, using Scratch, MIT’s visual, event-driven, programming environment.

I have not yet had any volunteers, though the flurry of online interest did get me to complete the first draft – so alpha testers still needed.

In the meantime, I have also published the version of Conway’s Game of Life the text is based around. It’s a slightly unusual implementation in that the surface of the game is, in effect, spherical in effect a torus – i.e. the edges are effectively a feature of the projection of the surface but left joins to right, top to bottom and so on.

Update: Been pointed out to me that this isn’t a sphere but a torus, and so I have updated the copy.

## A little plug for BINSIC

Thirty-three years ago my brother and I got a new cassette player for Christmas.

That allowed us to write and save games for our ZX80 computer (like many ZX80 owners we found that an older cassette player just didn’t work) and in 1981 I wrote a Z80 machine code version of Conway’s Game of Life – still my proudest programming achievement.

Last year I sought to complete the circle by writing an interpreter/DSL that mimiced ZX80 BASIC and called it BINSIC as “BINSIC Is Not Sinclair Instruction Code” and then wrote a BASIC version of the Game of Life (see the screenshot below).

So, if you are from that generation computer users, or even if you are not, why not give it a try – more details here: BINSIC

## Life and polyominoes

Update: It seems I got all this wrong (again!). See Hugh’s comment here

A little while ago I wrote of how I had challenged the children I work with in a Code Club to find the glider pattern in Conway’s Game of Life.

I suggested that, if they adopted an essentially random approach to putting down counters within one cell of existing counters they would need about three weeks of continuous work to find the solution as there are about 30,000 such patterns and I estimated it would take a minute, on average, to check the solution for longevity. (In fact I over estimated the average time by 50%, because, of course we should expect to trip over the correct solution, on average, at the half way point – if we adopted a truly random approach to this of course.)

Hugh who is a regular and learned commentator here then drew my attention to sequence A094169 in the “Online Encyclopedia of Integer Sequences” to suggest that there were only, in fact 3,230 possible solutions to be checked – as that is the number of five cell polyominoes (to be fair to Hugh he suggested that polyominoes were not the only potential solutions of interest).

In fact if we looked at polyominoes we would never find the solution – as the glider is not a polyomino – none of the five configurations has every counter/cell joined edge to edge.

But I am again forced to reduce the time – because there are essentially five glider patterns (or if you like any one glider pattern is isomorphic to four others) – and any one of them would do – so we are left with an expectation that we’d find the pattern in about 3,000 random tests – more or less the same number as the count for the pentominoes.

## Why I love Metapost

I am writing some stuff about Conway’s Game of Life (and Scratch) – thinking about whether it is possible to explain to adults the basics of programming a computer using the Scratch Life script an an example: Life is more suitable for adults than say the Code Club fish chasing game and anyway it gives me an opportunity to indulge my fascination with the game.

To write the text I need to draw diagrams that explain how the rules work and I tried in both Xfig and Dia to do this. But it was a nightmare.

In contrast I could manage it very quickly in Metapost, even though the natural inclination is to steer clear of that and stick with the “point and drool” GUI based alternatives.

beginfig(1);
prologues:=3;

for i=0 upto 4:
draw (0, i*20 + 10) — (100, i*20 + 10);
draw (10 + i*20, 0) — (10 + i*20, 100);
draw (200, i*20 + 10) — (300, i*20 + 10);
draw (210 + i*20, 0) — (210 + i*20, 100);
endfor;

pickup pencircle scaled 12;
draw (140, 40) — (150, 50)–(140, 60) withcolor red;
linejoin:=mitered;

path a, b, c, d, e, f, g, h, j, k, l, m;
a = fullcircle scaled 10 shifted (40,40);
draw a;
fill a withcolor green;
b = fullcircle scaled 10 shifted (40,60);
draw b;
fill b withcolor green;
c = fullcircle scaled 10 shifted (60,60);
draw c;
fill c withcolor green;
h = fullcircle scaled 10 shifted (60,40);
draw h;
fill h withcolor green;
j = fullcircle scaled 10 shifted (40,20);
draw j;
fill j withcolor green;
k = fullcircle scaled 10 shifted (60,20);
draw k;
fill k withcolor green;

d = fullcircle scaled 10 shifted (220,40);
draw d;
fill d withcolor green;
e = fullcircle scaled 10 shifted (240,60);
draw e;
fill e withcolor green;
f = fullcircle scaled 10 shifted (260,60);
draw f;
fill f withcolor green;
g = fullcircle scaled 10 shifted (280,40);
draw g;
fill g withcolor green;
l = fullcircle scaled 10 shifted (240,20);
draw l;
fill l withcolor green;
m = fullcircle scaled 10 shifted (260,20);
draw m;
fill m withcolor green;
endfig;

Gives me this: (actually the original EPS is better as it is a vector format and the PNG won’t scale in the same way)

Metapost is not widely known and under-appreciated.

## Improved “Life” for Scratch

I have done some work on my Scratch-based version of Conway’s Game of Life…

## The Art of Scratch, Code Club and the ICT curriculum

Regular readers will know I have something of a small obsession with Conway’s Game of Life – the classic “game for no players” based on cellular automata, and so, naturally enough, when I decided that I really had to write my own Scratch program from, err, scratch to sharpen up my skills for teaching children via Code Club, that is what I chose to write – the (not very sophisticated) results can be seen above.

My first conclusion is that Scratch is a truly awful tool for most programming tasks. I know it is not meant to be a general programming tool, but I quickly discovered that it is hobbled even when it comes to doing those things that one assumes, at first glance, it is set up to do – like drawing on the screen. Scratch actually has very, very limited functionality/expressive power when it comes to drawing graphics – being only able to handle pre-provided sprites (as first class objects) and using a pen which marks out one pixel at a time – thus one cannot (at least easily) find a way to draw anything beyond dots and lines on the screen in response to events.

If you run the above program using the Flash player provided by the Scratch site you will probably see one of the big downsides of that as outlines of the old crosses are left on the screen (the Java player does not have this problem but it is very slow in comparison).

From a teaching point of view I also find Scratch’s message-based system less helpful than an imperative `GOSUB` like approach: the children I work with, after many weeks, are still struggling with the idea that messages should drive actions (probably we should blame their instructor!) – I know this event-based style is more common in the real world, but I think teaching the idea of problem decomposition via subroutines or functions is probably more important educationally.

Yesterday I went to the first London Hackntalk and gave an impromptu (and so unprepared) and brief talk on my thoughts about teaching children to program – my experience with Code Club makes me rather less starry-eyed about mass programming education. There were a few responses from the audience which suggested I had not really got my point – that we would struggle to fully replace an ICT curriculum based on usage skills with one based on programming – as the audience continually suggested ways to get motivated and engaged kids into programming (rather than make it a mass participation thing), but one point that was made by a member of the audience was very acute – given what our children see computers do in games that cost many millions to develop, how realistic is it to expect all or many of them to put lots of effort into toy programs that chug out the sort of graphics you can see above? I think that is a really difficult issue we have to consider when overhauling the curriculum and I am not sure the enthusiasts of radical change (of which I was and still am one) have thought it through fully.

(I did also encourage them to be Code Club instructors and was a bit disappointed to see that I appeared to be the only one – we urgently need to teach more programming and so these problems of the early days of the overhaul should not obscure the need for change.)

## The wheels of Aristotle

Sometimes you come across a thing where beauty matches simplicity, and Aristotle’s Wheel Paradox is just such a thing.

I came across it this afternoon after I returned to London from two too-short weeks away and a second-hand book I’d ordered, Wheels, Life and Other Mathematical Amusements, based on Martin Gardner‘s columns for the Scientific American.

I bought it because it has three chapters on Conway’s Game of Life – but the very first pages introduced me to Artistotle’s Wheel Paradox – which I’ll now explain…

Imagine, as in the diagram above a small wheel that runs in parallel (eg., because it is attached) to a larger wheel. The large wheel runs on the line A to B, the smaller runs on C to D.

At every point the large wheel touches the line AB, an equivalent point on the small wheel touches CD: so there is a fixed and unique equivalent point on the small wheel for every point on the large wheel.

So that means when the large wheel has completed a revolution then so will the small wheel.

But if there is a fixed and unique equivalent point on the small wheel to every point on the large wheel that must surely imply their circumference is the same?

This is the paradox. And it’s one that puzzled many of the mathematical greats of past ages.

The solution is down to Georg Cantor and his formulation of the continuum. For there are an uncountable infinity of points on the rim of the two wheels. (Gardner describes this as Cantor’s Aleph-One$\aleph_1$ – and indeed Cantor thought it so – this is his continuum hypothesis – but it remains unproven that the continuum is indeed $\aleph_1$ as opposed to a higher $\aleph$.)

One final note – the book I bought is stamped “University Library Hull Withdrawn” and an online search suggests that this book is indeed no longer available to students at Hull. But how can it be justified that a major university gets rid of books in this way? Their loss, my gain though, of course.