Adventures of a Shivanaut

[Yes, this post is all about mathematics and patterns.  If that sounds horrific, please feel free to skip it.  If you want though, I've created a new Level 3 pattern for you to try at the bottom.]

Why would you write about this?

My handle is the Dancing Geek.  The geek part is not just for show – I have a degree in this stuff, and sometimes I actually enjoy solving unnecessary puzzles just for fun.

The theory behind Level 3 as a mathematics puzzle

I’ve made up some notation to keep this shorthand.  H is horizontal, V is vertical and the number relates to the position.  So H1:V1 is left arm in Horizontal 1 position, right arm in vertical 1 position.  Clear?

1 complete round (i.e. you get back to the starting position and are ready to go on the opposite side) is 16 moves at Level 3.  It breaks down into 4 repetitions of the same 4 moves (i.e. the instructions are the same).  Looking at where your arms are after each of these 4-move combos for the first starting position gives us the pattern:

H1:V1 to V1:H3 to H3:V3 to V3:H1 to H1:V1

This can be generalised (using algebra – yippee!) to:

Hx -> Vx

Vy -> Hy+2

In words:

A horizontal starting position will end with that arm in the same position on the vertical plane.

A vertical starting position will end with the arm in the transquartered position on the horizontal plane.  (Hy+2 uses modulo 4 arithmetic, in case you weren’t clear).

How does it work?

Another way of looking at it would be to say that the movement swaps the positions of the arms, moves the right arm 2 positions on, and swaps the planes of the arms.

Either way, the most important aspect of the pattern is that it has symmetry 4.  That is after 4 repeats it returns to where it started.  Simple example of this would be a rectangle with a dot in the corner being turned 90 degrees clockwise:

A brand new level 3 pattern!

Yes, I have created a new pattern which I am calling Level 3 because it works in a similar fashion.  Since I don’t know about anything higher except for a bit of Level 4, I could be talking complete and utter bull.  Blame @Sari_O for getting the idea stuck in my head.

It goes:

• Transquarters
• Mirror reflection
• One forward, one back
• Mirror reflection

Or, you could do:

• One forward, one back
• Transquarters
• One back, one forward
• Both forward

Not sure if I’ll try these or not.