GMU:BioArt WS15/Xianzhi Zhang: Difference between revisions

The more complex patterns must be constructed from a set of basic patterns. The “Golly Ticker” is also no exception. Let’s see what it does first.  

Load it from under the menu 'Patterns/Life/Guns/golly-ticker.rle' in the left panel and play it. You should see the word “Golly” (with a stylized “o”) move across the screen and then disappear at the left. This process continues infinitely, just looks like a stock ticker.

First, let's start with the Life objects that make up the text "Golly". The text is made up of what is known as the “Light Weight Space Ship” or LWSS for short. These Life objects continuously move in one of the four directions — up, down, left or right but never diagonally. Their speed is often expressed as a fraction of “c” or the speed of light. The speed of light taken in the context of Life refers to advancement of one cell per generation and this is the fastest a Life object can move.

The “Glider” (mentioned above) can move only diagonally at c/4 whereas the LWSS can move orthogonally at c/2. We can easily verify this using Golly, running slowly enough to clearly see the movements of each generation.

Each letter is 9 LWSSs in height, except for the "O" which is 11 LWSSs in height. If you take a close look at the characters, not all LWSSs are in the same phase. Some seem to "point" downwards and the rest upwards.  

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At the left end, there are structures called "Eaters" or “Fishhook". Just flanked one either side by them are the patterns known as "Kok's Galaxy".

Eaters are “Still Lives” which can eat away many objects without sustaining permanent damage. The job of the eater here is to assimilate the LWSSs coming in from the right. Since we have two distinct phases of LWSSs, the eater must be oriented properly to perform its job, otherwise the LWSSs will permanently destroy the eater.  

Kok's Galaxy belongs to the class of oscillators. Functionally, the generations of Kok's Galaxy flanking the eaters don't serve any purpose since deleting them doesn't affect the ticker at all.

The text is generated row by row. It starts by first creating the rows in the middle — the sixth and seventh rows. Rows 1 to 6 are created by the six structures at the right-top which are called “memory loops”. The other five are created by the five memory loops at the right bottom. The memory loops hold a specific pattern made of gliders that keep looping in the structure. At one end, they are duplicated where one glider is fed to the "Converter" and the other back into the memory loop.

The gliders loop following the yellow arrows with the help of “Reflectors” placed at either ends. Additionally at the bottom end there is a glider duplicator. It produces a glider that moves parallel to the original. While the duplicated glider is sent back into the loop, the original glider is sent to a “Converter” which converts the glider to a LWSS (moves along the first red arrow). Following conversion, the LWSS takes the path of the second red arrow, to become one pixel of a row. All of the memory loops work in the same way and are slightly displaced in height to produce LWSS in separate rows.

It is possible for gliders to interact with other objects in interesting ways. For example, if two gliders are shot at a block in just the right way, the block will move closer to the source of the gliders. If three gliders are shot in just the right way, the block will move farther away. This "sliding block memory" can be used to simulate a counter.

It is possible to construct logic gates such as AND, OR and NOT using gliders. It is possible to build a pattern that acts like a finite state machine connected to two counters. This has the same computational power as a universal Turing machine, so the Game of Life is theoretically as powerful as any computer with unlimited memory and no time constraints: it is Turing complete.

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"The finite state machine part can clearly be seen as the square pattern in the bottom left of the picture. This has an addressing mechanism on the left (state value) and at the bottom (symbol value) and nine memory cells to hold the data table to describe the action for each combination of the internal state and symbol values.

The Turing Machines tape is represented by the two stack mechanises seen extending top left and bottom right. Each stack cell can trap 3 gliders using the kickback reaction. This is the reaction that turns a glider through 180 degrees when encountering another at right angles. The traps can be seen as empty rectangles between the denser patterns in the cells. These denser patterns delay the transit of the gliders from one cell to the next so that the destination cell is empty when they arrive. The control signals for the cells travel up the sides of the stack.

Between the two stacks is the logic to perform serial to parallel and parallel to serial conversion and generate the stack control signals so that one stack performs a push operation and the other performs a pop operation.

The other item visible is the delay loop for the next state which extends from the centre towards the left top corner underneath the left stack. The next state value is copied from the data read from the finite state machine and sent round this loop to address the finite state machine for the next cycle in conjunction with the symbol popped from one of the stacks." (Paul Rendell, 2011)

https://github.com/ormanli/Rule-110