Pow 16: Spiralaterals

A spiralateral is a series of line segments that form a shape that resembles a spiral. You make spiralaterals by picking a spot on a piece of graph paper to be the starting point of the spiralateral. Then take a set of three numbers and using that point go up the first number of squares on the graph paper, go right the second number of squares, down the third number of squares and left the first number of squares going in that pattern until the line meets the starting point. So if you were using the numbers 1, 2, and 3 you would do what is shown in the diagram below. You go up one square, then you go right two squares, next you go down three squares and start the sequence again but while going in that direction. So after you go down three you will go left one and then up two and you just keep going in that same pattern.

When I started my series of spiralaterals I started with trying to find out what would happen when you switched the order of the numbers and I saw a pattern. The concept I explored using spiralaterals was whether or not changing the order of the three numbers of the sequence would change the shape, size or view of the spiralateral.

My initial ideas about spiralaterals when I first saw them was what they would look like when you changed the order of the numbers and whether or not they would always connect. I thought that if the order was changed maybe the general shape of the spiralateral would change or the shape maybe would become wider or taller. Also I was wondering if you used certain numbers or the same number twice whether or not it would connect. The method I used to explore my concept was to pick three numbers and make spiralaterals for all the possible combinations of those three numbers. So I made spiralaterals for 1-2-3, 1-3-2, 2-1-3, 2-3-1, 3-2-1 and 3-1-2 and saw what it did. Also I threw in some random number combinations just to see what it would do and because I was bored with doing them in order. While doing this POW and exploring the different concepts I didn't run into ant problems so I had none to solve. The only assistance I had was when I was when asking people to give me three random