We don't need to do types starting with "L" since you can replace all "R" for "L" and vice versa to obtain the same result (flipped over the vertical axis)
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RR -
RL highway
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RRR -
RRL highway
RLR chaos
RLL chaos
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RRRR -
RRRL highway
RRLR highway
RRLL symmetry (tends to a cardioid)
RLRR chaos
RLRL highway
RLLR symmetry (almost-square frame, lots of one color)
RLLL chaos
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RRRRR -
RRRRL highway
RRRLR chaos
RRRLL chaos
RRLRR highway (square)
RRLRL chaos
RRLLR chaos
RRLLL chaos
RLRRR chaos
RLRRL chaos
RLRLR chaos
RLRLL chaos
RLLRR chaos
RLLRL chaos
RLLLR chaos
RLLLL chaos
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RRRRRR -
RRRRRL highway
RRRRLR chaos
RRRRLL symmetry (chaos)
RRRLRR chaos
RRRLRL chaos
RRRLLR symmetry (chaos)
RRRLLL highway
RRLRRR chaos
RRLRRL highway
RRLRLR chaos
RRLRLL chaos (blocky though)
RRLLRR symmetry (chaos)
RRLLRL chaos
RRLLLR chaos
RRLLLL symmetry (chaos)
RLRRRR chaos
RLRRRL highway (square)
RLRRLR chaos
RLRRLL chaos
RLRLRR chaos
RLRLRL highway
RLRLLR chaos
RLRLLL chaos
RLLRRR symmetry (semi-chaos)
RLLRRL chaos
RLLRLR chaos
RLLRLL chaos
RLLLRR semi-chaos
RLLLRL semi-chaos
RLLLLR symmetry (semi-chaos)
RLLLLL chaos
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Couple of cool ones from wikipedia
LRRRRRLLR
LLRRRLRLRLLR
RRLLLRLLLRRR
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Sequences of R and L alternating seem to get to a highway from RLRLRLRL and longer
RLRLRLRLRLRLR is a nice one
RLRRRRRLR sure is an interesting one. Put more R's between the two L's to obtain a similar result. I don't know if they all form a similar square, e.g. RLRRRRRRRRRRRRLR stays very small
RRLRLRR weird triangle highway
RRLRRLRR highway
RRLRRRLRR chaos
RRLRRRRLRR square highway
...
RRLRRRRRRLRR square highway
RRLRRRRRRRLRR chaos?
RRLRRRRRRRRLRR square highway
...
RRRLRRLRRR triangle highway
RRRRRRRRRRLRRRRRRRRRLRRRRRRRRRR WHAT THE HELL