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I am working the a subject guide on involving $L$-Systems and have the alphabet $A = \{a, b, c\}$. The initiator is the string $a$ and the rules of substitution $a \to ba$, $b \to ccb$, $c \to a$.

The study guide gives the first five generations as:

$$[a] \to [ba] \to [ccba] \to [acba] \to [aaba] \to [aaccba]$$

I can't for the life of me figure out how this works. No rules regarding the order of substitution are provided, and my lecturer say's that it is possible to get to this.

Does anybody have any ideas?

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Generally, all of the substitutions are assumed to occur simultaneously. The thing is, the chain of generations you've given doesn't seem to follow the rule (for example, [ba] should go to [ccbba]). Are you sure you copied down the information from the study guide correctly? – Will Dana Feb 23 '12 at 16:42
I am afraid so. Checked and double-checked. – Ray Feb 23 '12 at 17:45
up vote 1 down vote accepted

It looks like only one symbol is substituted in one step. The symbol $c$ gets highest priority, followed by $b$ and then $a$. When there are multiple instances of the same symbol, the leftmost is changed. But of course this is guessing, and the example is too short to allow much confidence.

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I agree with this nukka. – Hautdesert Feb 26 '12 at 3:31

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