Unexpected behavior of C2mm symmetry.

#openuniversity# #m336# #symmetry#

I read that a US Senate Commission is worried about the F-35 project because they are building planes while the testing of the F-35 is in full progress. The thing is that the Joint Strike Fighter ( F-35 ) is in fact a flying super-computer running on state-of-the-art software. Sound engineering principles don't apply to these machines. Software is never 'done'. Software is always in development and in testing and ( just ) released at the same time. There will be upgrades for the F-35 until the end of its life. Politicians think ( or say they think ) that when the plane is done, its done.

This thought crossed my mind because planning, by definition, implies uncertainty about the future. Unexpected things can happen, will happen, at a moment when its least expected.

To the point.

Mathematics is unpredictable too. From time to time you'll see unexpected things. Among various other topics I am studying plane symmetries at the moment. I have several books well illustrated with all sorts of patterns that can occur. For me, programming is an effective way to study, so I wrote a program that plots patterns using the symmetries I am studying. One of these symmetries is C2mm which is basically rotating a diamond lattice 90, 180, 270 and 360 degrees. While I was testing the C2mm symmetry in Graphica ( the name of my symmetry program ) I noticed that the patterns are very sensitive to the center of rotation.

I made a video ( of only part of the screen for size and performance reasons ). The second half of the video shows several unexpected patterns while changing the center of rotation. Watch and you may experience the same awe that I felt. All I expected was that the symmetry could generate a diamond lattice from a triangle.