Viral Spirals
Introduction
In today's lesson, you will be representing a sequence of numbers on squared paper (or geogebra) to create ‘cyclic’ geometric patterns.
The picture on the right shows a 1-3-2 viral spiral. What do you think this means?
Viral spirals obey the following simple rules:
Go to first number in code.
Draw line of length of that number.
Rotate 90º clockwise.
Move to next number in code and repeat steps 2 to 4.
When you get to the end of the 3 code list, return to first number and repeat steps 2 to 5 until there is a good reason to stop.
Look at this video to see how it works. If you understand it, try a different code.
Investigation
Investigate different 3 digit spiral-virals, using only the digits from 1 to 4. Record anything interesting you notice.
Here are some questions should you want a prompt:
How would you describe the patterns produced?
How many line and rotational symmetries are there?
Some codes produce the same pattern. Which ones and why?
What happens if a digit is repeated?
Can you find all of the codes that produce the same pattern?
Will viral spirals-always link up?
Further Questions and Challenges
Here are some further ideas to investigate:
What if you use 3 digit codes with digits 1 to 9 instead of 1 to 4? What changes?
What if you have 4 digit codes instead of 3 digit codes?
What if you have different number of digit codes, i.e 2, 5 etc digit codes?
Can you come up with codes that produce patterns with rotational symmetry only? What is common about these codes?
Can you come up with codes that generate patterns with different numbers of line symmetry? What is common about these codes?
Can you come up with codes that will generate grids like the one on the right and others? What is common about these codes?
Which number digit codes will link and which won’t. Why?
What can you change to produce polygons?
Extension
Explore changing the angles and have a go at this logo game on transum. To learn more, take a look at these lessons on Turtle Academy.