Coloured symmetry or Magnetic groups

Colour conscience is quite important in designs as well as in science. Let us take the bottom paisley design that I made in http://www.ikolam.com/node/6030?p=1930 Let us try to make this design with two colours, usually black and white. Or the objects can have up and down characteristics with directionality like the magnetic moment. In fact such symmetries are called magnetic symmetry groups. For the sake of esthetics, I am choosing two paisley designs in cyan and pink. They are always taken in pairs so that the number in each is always even (zero is an even number). There are six possibilities shown in the accompanying figure. The first line is all pink and the second line is all cyan. These are quite easy to understand. The symmetry in these is the full symmetry (horizontal mirror, vertical mirror and a 180 degree rotation). In the third line, we have alternately pink and cyan. To get consecutive pink or cyan sets, one has to travel twice the distance of the first two. In the fourth one, the horizontal mirror is the true symmetry. For the vertical mirror and the 180 degree rotation, the colours are interchanged. In the fifth one, the vertical mirror is the true symmetry. The horizontal mirror and the 180 degree rotations reverse the colours of the paisley. In the sixth (and the last) one, the true symmetry is 180 degree rotation. For the two mirrors, the colours are reversed. This is a simple case of two colours and one dimension. Herein we have such complexities. For more number of colours and higher symmetries, there is certainly more conceptual difficulty. This is the reason why I often stress on the symmetry. This is not to offend my esteemed friends or to criticise their true works of art. I apologise to anybody if so offended. Regards! - mOhana