e c a   s e e d s

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The first step in setting up an eca is to define the initial conditions against which the rule will start running. This is called the seed row. The first row generated by the rule is designated as row 1.

The classic eca uses a single seed as the starting condition. As shown below, the cells are generated by only four of the possible eight blocks:

• Block 0 (000): the majority of the cells to the left and right
• Block 1 (001): to the left of the seed
• Block 2 (010): replaces the seed
• Block 4 (100): to the right of the seed

					S
0	0	0	0	1	2	4	0	0	0	0

 

To overcome this limitation, I also use a couple of seed conditions which ensure that each block is is used to generate the first row at least one time.

Multiple seed 1 (m1):

			S		S	S	S		S				S	S
0	0	1	2	5	3	7	6	5	2	4	0	1	3	6	4	0	0

 

Multiple seed 2 (m2):

			S	S				S		S	S	S		S
0	0	1	3	6	4	0	1	2	5	3	7	6	5	2	4	0	0

 

Here's a chart comparing single seed and m1 seed.

I also use a series of seed conditions to study the incremental impact on patterns:

Seed 1 (s1)					S
Seed 3 (s3)				S	S
Seed 5 (s5)			S		s
Seed 7 (s7)			S	S	S
Seed 9 (s9)		S			S
Seed 11 (s11)		S		S	S
Seed 13 (s13)		S	S		S
Seed 15 (s15)		S	S	S	S

 

Note that all these are odd numbers because the even numbered seeds will generate the same result as an odd numbered seed:

• Seed 2 (010), Seed 4 (100), and Seed 8 (1000) will generate the same result as Seed 1
• Seed 6 (110) and Seed 12 (1100) will generate the same as Seed 3 (011)
• Seed 10 (1010) will generate the same as Seed 5 (101)
• Seed 14 (1110) will generate the same as Seed 7 (111)

And here's some charts comparing these seed conditions: Rules 000 - 063, Rules 064 - 127,
Rules 128 - 191, Rules 192 - 255.

Finally, there are complex seeds which were either drawn from another researcher’s work so I can compare results or are totally arbitrary (from random.org).