Page 23 - Studio-International-January-1974

with exactly the same result. Note how
powerful a device it is that instead of saying
first 'print the square of i', then 'print the
square of 2', then 'print the square of 3', we
need only say, 'print the square of whatever is in
the cell labelled COST', repeating the same
instruction every time. All that changes is the where the cell PEN will hold r as a code for 'pen
contents of the cell COST. This notion of down' and o as a code for 'pen up'. We might
referring to a number by the name on its cell is also have generalized a step further, and said:
fundamental to programming, and in fact it is
something we do all the time ourselves. Saying
that a carpet is ten feet long and seven feet wide
is essentially like saying :

because now we might want to write the sort of
reiterative programme we looked at earlier, to
draw a whole series of points. In writing such
a programme we will now use a shorter notation
for PUT, so that instead of writing PUT 5 in
HOZ, we would write HOZ <— 5.
Figure 7
The thing is that any pair of statements which
relate the horizontal coordinate to the vertical in
a coherent way will produce some sort of curve,
and it's quite easy at this point to start popping
in all kinds of trigonometrical functions and
stand back to see what happens. This one was
written by a passing computer-science student —
I hesitate to say 'invented', since it is almost
entirely a matter of chance whether it will
produce anything pretty, which I think it
•
does.
the important thing here is the level of
generality, since the programme will now work
for whatever values we put in the cells labelled
LENGTH and WIDTH.
We should be able to get the drawing
machine to draw something now. You will
probably remember the idea that you can
describe the position of any point on a sheet of
paper by two distances, or coordinates : how far
the point is horizontally from the left hand edge
and how far it is vertically from the bottom.
Suppose we were to reserve two cells labelled
HOZ and VERT for storing the two
coordinates for any point to which we wanted
the pen to go. If the pen is sitting in the bottom Figure 6
left hand corner, and our programme says :
Not a very exciting drawing, but it does
illustrate a lot of principles. You might be
surprised by the statement
<-- HOZ + 5
HOZ
but of course this isn't algebra, and it isn't an
equation. It means, simply, 'take what was in
the cell labelled HOZ, add .5 to it and put it
the computer will recognize from the command back in the same cell'. The pen has drawn a
MOVE that it must send its instructions to the series of ten short line segments which in this
drawing machine, not to the teletype, and will case make up a straight line: and has then
thus send out the commands required to make lifted and gone back to the bottom left hand
the pen move to the centre of the bed. The only corner. The same general form will draw lines
problem with this programme is that it didn't which are not straight, if we can simply think
specify whether the pen was to be down or up. of a way of generating the appropriate pairs of
The programme should probably have read: coordinates. For example: Figure 8
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