31. Starting at the point (1/2,1/2) applying either rule 3, (x,y)->(x/2,y/2), or rule 1, (x,y)->(x/2 + 1/2,y/2 + 1/2), gives a point on the line between corners 1 and 3. In general, starting with a point on this line and applying either rule 1 or rule 3 gives another point on this line. So starting on the line and applying just these rules generates only points on this line. (What happens if we start with a point not on this line, but still apply only rules 1 and 3?)

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