IFS with Memory

Reducing memory from 2-step to 1-step

Recall the order in which the forbidden and allowed triples of two step memory are presented,
we see that in order to allow the pair i → j, we must allow all triples
1 → i → j, 2 → i → j, 3 → i → j, and 4 → i → j.
We write this with the shorthand
* → i → j
Looking at the orders of the row, column, and face lables, we see this 1-step IFS and 2-step IFS will produce the same pictures. Click each table to see the corresponding picture.
 
Here are two examples made with 1-step memory. Find the corresponding 2-step memory tables and test them with the software. Click each table for the solution.
Based on these examples, you should be able to formulate a condition guaranteeing a 2-step memory table will produce a picture that can be generated by a 1-step memory table. From this, can you find 2-step memory pictures that cannot be generated by 1-step memory? Test your ideas with the software, then click here for an answer.

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