Random patterns

Pasang Emas comes with 6 buttons to generate random patterns. The pattern generator behind these buttons is programmed to produce patterns with the same kinds of symmetries found in the traditional patterns, except for finer symmetries within 6x6 quadrants, though such symmetries may arise purely by chance. The generator is also programmed to produce other kinds of symmetries not found in the traditional patterns.

A technique employed by the generator that works rather well in composing pleasing patterns is to intentionally break an otherwise highly symmetrical arrangement.

The following are samples created by the pattern generator. Some are worthy rivals of the traditional patterns.


Square symmetry

The first pattern generator button is configured to produce patterns with 4 mirror axes, as shown in these samples:

The patterns in the first 2 rows have quadrants with 4 mirror axes. The ones in the first row are night-and-day arrangements where the pattern and its background form the same shape. The third row shows patterns having quadrants that are diagonally symmetrical. The fourth row shows patterns that almost belong to the first 2 rows, but their symmetries are broken in the centre. The last row lacks finer symmetries.


Night-and-day symmetry

The second button produces night-and-day patterns with a 4-fold symmetry. Here are some samples:

4-fold symmetry

The third button issues patterns with a 4-fold symmetry, such as these:

The first row shows patterns with quadrants having their own symmetries. The second row shows patterns that almost have mirror symmetries, but are broken.


Horizontal and vertical symmetry

None of the traditional patterns currently known to Pasang Emas have only horizontal and vertical mirror axes. The fourth button fills this gap, creating patterns such as these:

The patterns in the top row have symmetrical quadrants or symmetrical halves. The patterns in the middle row are almost diagonally symmetrical.


Diagonal symmetry

The fifth button composes diagonally symmetrical patterns, such as these:

In the first row, quadrants are translational images of each other. The second row shows patterns with broken horizontal and vertical symmetries.


2-fold symmetry

The sixth button produces 2-fold symmetrical patterns. A 2-fold symmetry is the least symmetrical arrangement that still fairly divides the playing pieces between the top and bottom halves of the board. Here are some samples:

The patterns in the top row have symmetrical quadrants or symmetrical halves. The second row exhibits patterns that almost have further symmetries.