Take some negative numbers too
Graphics[Line[AnglePath[N[Flatten[SubstitutionSystem[
Rule[#[[1]], {RandomChoice[{-1, 1}] #[[2]]}] & /@
Partition[First[RealDigits[N[E, 30]]], 2],
First[RealDigits[N[E \[Pi], 133]]], 31]]]]]]
and one symmetrical (despite the pesudo-randomness in the rule, it's only active during rule creation)
Graphics[Line[
AnglePath[
N[Flatten[
SubstitutionSystem[
Rule[#[[1]], {RandomChoice[{-1, 1}] #[[2]]}] & /@
Partition[First[RealDigits[N[Pi, 30]]], 2], {7, 3, 2, 8},
304]]]]]]
giving
replace
$\pi$ again with
$e$
Graphics[Line[AnglePath[N[Flatten[SubstitutionSystem[
Rule[#[[1]], {RandomChoice[{-1, 1}] #[[2]]}] & /@
Partition[First[RealDigits[N[E, 30]]], 2], {7, 3, 2, 8}, 304]]]]]]
and hit the return key a few times to see