ULAMIZER-II : Some Example Trigger Sequence Patterns

D Burraston

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Each CA cell in the ULAMIZER-II module can output a trigger pulse and a programmable MIDI NOTE message (other MIDI messages such as CC, SysEx strings will be added).

Black = Trigger Pulse On / MIDI note on / LED on

White = Trigger Pulse Off / MIDI note off / LED off

Below are some animated gif sequences of CA evolutions. Instead of spacetime patterns, just the row of CA cells are shown, and the evolutions are seen as an animation. Each cell corresponds to a trigger output. This is the pattern seen on the trigger outputs and LED display of ULAMIZER-II.

 

Using a single active cell as the seed, rule 240 emulates a standard trigger sequencer (left to right), e.g. for an 8 cell CA :

 

Using a single active cell as the seed, rule 170 emulates a standard trigger sequencer (right to left), e.g. for an 8 cell CA :

 

Using a single active cell as the seed, alternate between rules 170 and 240 for "pendulum" mode. The rule switches over at each end of the sequence :

 

Using an arbitrary pattern as the seed, rule 240 shifts the pattern left to right, e.g. for a 16 cell CA :

 

Using an arbitrary pattern as the seed, rule 170 shifts the pattern right to left, e.g. for a 16 cell CA :

With rules 170 & 240 we have the added benefit of setting up any trigger pattern and it will cycle that pattern around as long as the system is clocked. We can see that all patterns of rule 170 & 240 are shifted by looking at an example of the basin field view for an 8 cell system, equivalent to an 8 step sequencer. The attractor cycles show that all the shifted patterns are located within the same attractor cycle. A standard trigger sequencer is equivalent to the cycle containing just a single active cell.

 

Its that simple. If you want a 32 step pattern sequencer, setup ULAMIZER-II with 32 cells, 4 cells for 4 step, 11 cells for 11 step, 128 cells for 128 step etc. Trigger sequencing with ULAMIZER-II can go far beyond simple emulation of a standard sequencer step or rotating a pattern, by simply changing the rule. A variety of example trigger patterns for the more popular elementary rules are shown below. Two examples are given for each rule :

i) from a random seed

ii) a single active right cell as seed

 

Each animation shows 16 generations (i.e. the CA is clocked 16 times) and then the animation repeats. The ULAMIZER-II module can continue running the CA as long as it is turned on and clocked (via an analogue gate/trigger or from the MIDI clock, both with a wide clock division range). Note that rules 18, 210 and 22 evolve to all zero's (all triggers off) from a single seed, this is class 1 ordered behaviour.

 

rule 30 (equivalent to feedback shift register circuits) :

Random Seed

 

Single Active Right Cell as Seed

 

rule 105 :

 

 

rule 126 :

 

 

rule 150 :

 

 

rule 18 :

 

 

rule 210 :

 

 

rule 225 :

 

 

rule 22 :

 

 

rule 45 :

 

 

rule 54 :

 

 

rule 60 :

 

 

rule 62 :

 

 

rule 73 :

 

 

rule 110 with 64 cells (running for 64 generations) :

 


Moving beyond the elementary rules into the 4 or 5 neighbour rule space gives a huge variety of ordered, complex and chaotic pattern generation. From a simple trigger sequencer we end up with unlimited pattern for free. Some complex rules using 64 cells are shown below starting from random seeds and running for 64 generations. The animation is then repeated from the seed state. The ULAMIZER-II module can continue running the CA as long as it is turned on.

 

4ad95ee0 :

 

506cf09f :

 

52180643 :

 

6f1de091 :

 

912aef98 :

 

c251d668 :

 

d598ad7a :