Number Art: Drawing Spirals with Multiples
Connect multiples of a number around a circle of evenly spaced dots, and the repeating pattern the leftovers make draws a spiral.
- Paper
- A pencil
- A ruler, and a compass or a round object to draw round
- Colored pencils or markers
Draw your spiral
- Draw a circle. Use a compass, or trace round something circular. Bigger is easier.
- Mark the points. Make evenly spaced dots all the way round the edge, then number them 1, 2, 3 and so on. Thirty dots is a good number to start with.
- Choose your multiple. Pick a number to multiply by — 2 is a good first choice.
- Connect the first pair. Start at dot 1. Multiply it by your number: 1 x 2 = 2. Draw a line from dot 1 to dot 2.
- Keep going. Now do the same from dot 2: 2 x 2 = 4, so draw a line from dot 2 to dot 4. Then 4 x 2 = 8, and so on.
- Wrap around when you run out. If an answer is bigger than the number of dots, keep subtracting the total until it fits. With 30 dots, an answer of 32 becomes 32 - 30 = 2, so you draw to dot 2.
- Stop when you come back round. Sooner or later a line takes you back to a dot you have already left from, and the pattern closes.
- Color it in. Fill the spaces the lines have made, or shade from one color to another across the shape.
Why a pattern appears at all
You are doing two things over and over: multiplying, and then wrapping around when the answer runs off the end of the circle. Wrapping around is really just asking "what is left over?" — and leftovers repeat. Because they repeat, the lines repeat too, and repeating lines are what your eye reads as a pattern.
A ring of dots, and one number to change: the step. Count on by it from the top dot, draw a line to whichever dot you land on, and keep going until you are back where you started. A bar along the foot of the sheet grows for every step you try, showing how many dots that step landed on. On a ring of twenty-four, twenty-three is the biggest step there is — see whether it draws the biggest figure.
Try this next
- Different multiples. Try 3, then 4, then 5. Each one draws a completely different shape from the same dots.
- More dots. Sixty dots instead of thirty gives you a much finer pattern.
- A different outline. Try the same rule with dots round a square.
Two people can follow these exact steps, pick different multiples, and end up with drawings that look nothing like each other.