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How about making designs like the ones above?
It's just a matter of getting a group of numbers together that
repeat and then using a simple drawing rule, then colouring the
A good way to start is to take a number sequence that you like, for
example square numbers or the $3$ times table.
Just keep the ones (units) of those numbers, for example $1, 4, 9,
6, 5, 6, 9, 4, 1, 0, 1, 4$ etc. or $3, 6, 9, 2, 5, 8, 1, 4, 7, 0,
3, 6$ etc.
You may notice that with these, and perhaps your own sequences,
they go to a $0$ and then repeat.
For this challenge, you just need the numbers that go as far as
just before the zero, for example $1, 4, 9, 6, 5, 6, 4, 1$ or $3,
6, 9, 2, 5, 8, 1, 4, 7$.
Now to draw ...
Using squared paper and starting somewhere in the middle, take each
of the numbers in turn to tell you how long to draw the line and
turn a right angle to the left after you've drawn each line.
This may help you to see what to do, using the example of square
numbers and starting with the red $1$. I've coloured each new line
with a different colour:
After the final $1$ you start again as shown below:
and so on until you get back to the beginning.
Some squences that you choose may not come back to the start but
just keep stepping away!
So now it's your turn ...
Choose your sequence.
Pick out the ones (units) until you find it repeating.
Draw the lines carefully on squared paper turning in the same
direction each time by a right angle.
See what you get and colour it in if you like.
You may like to change a rule or two after a while. (For example,
you could change the turn to $60^\circ$ instead of
Please send us your pictures.