بسم الله الرحمن الرحيم

May 24, 2010

How it really looks like

A primary school teacher posted this blog entry containing many pictures showing pasang boards the way they are traditionally made. Notice the "cup" in the middle of each board. This cup, called "gadong", plays no part in the game. The first player is supposed to accumulate her bounties in there, while the second player puts hers on the table. The game is in no way affected if this purely ornamental rule is not observed. In fact this cup actually blocks from view pieces near the centre.

When I learnt pasang, my mentor lent me a set with wooden pieces. I think that's the way they were traditionally made. But the bulky wooden pieces, which must have been a hassle to make, gave way to the more convenient and cute coat buttons, conveniently available at the nearest supermarket at a very affordable price. Two themes in an early version of Pasang Emas parodied this button-using trend. Notice in some of the pictures the use of red and bluish buttons for the kas. Red and blue combination is a convention introduced by Pasang Emas.

Jabatan Muzium-Muzium (Department of Museums) published reference cards showing traditional opening arrangements. You can see these cards in some of the pictures.

A secondary school posted this blog entry showing pictures of students learning pasang. Here again we can see the unmistakable traditional board dotted with tailor buttons. The man with the white cap must be the instructor. Indeed he must be. He is my pasang mentor.

May 17, 2010

Create your own opening patterns

Pasang Emas version 2.1.0 has a new feature. It is now possible for players to create their own opening patterns. Clicking the menu item [Game | Custom Patterns] opens up the pattern editor.


The editor is so simple that I didn't bother to write a user guide for it. You may create as many patterns as you wish. Each pattern must consists of exactly 60 white pieces. To use the patterns simply click [Apply].

The screen shot below shows a game opening using a custom-made pattern.


Here are some patterns that I composed:


All of them, except the last two, have symmetrical 6x6 (overlapping) tiles. Some are "pairs" that use the same tiles but arranged differently. The first pattern also has a night-and-day symmetry where the pattern and the background form the same shape.

May 10, 2010

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.

May 2, 2010

Symmetries in traditional patterns

There are more than 30 traditional patterns to start a pasang game. All of them exhibit some forms of symmetry.

Perfect symmetry

The following pattern is the most symmetrical. In traditional embroidery, it is used for dithering.

Square symmetry

Most traditional patterns have mirror symmetries with 4 axes, such as these:


Among such patterns, some have finer symmetries in their quadrants. The following have diagonal symmetries in their 5x5 quadrants. The last one also has vertical and horizontal symmetries in its quadrants.


The following pattern is rather unique. Apart from the perfectly symmetrical dithering pattern, it is the only traditional pattern having 6x6 (overlapping) quadrants that are diagonally symmetrical.


4-fold symmetry

Some patterns have 4-fold (90-degree rotational) symmetry, such as these:


A few of such have almost mirror symmetries, but they are broken in the centre.


Diagonal symmetry

One particular pattern has only mirror symmetries diagonally.


Night-and-day symmetry

Two patterns have night-and-day symmetry where the pattern and the background form the same shape of different handedness.


Building unit

A few patterns are made up of units larger than "dots". In particular, the following patterns are made up of, respectively, v's, w's and pluses.