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 2 added output edited Apr 12 '16 at 8:11 Martin Ender 6,77911 gold badge2424 silver badges5353 bronze badges You could try something like this: Show[Graphics[{RandomColor[], Line[#]}] & /@ ( (* Make graphics of *) FoldList[Plus, RandomReal[{0, 0.1}, 2] + {0, 0}, #] & /@ (* Trajectories built from *) Permutations[ (* All possible orderings of *) Join @@ ({{0, 1}, {1, 0}} & /@ Range[5]) (* Five steps N and five steps E*) ] )]  The RandomReal[{0,0.1},2] is a random near-the-origin starting location, just to offset the different lines from one another visually. You could try something like this: Show[Graphics[{RandomColor[], Line[#]}] & /@ ( (* Make graphics of *) FoldList[Plus, RandomReal[{0, 0.1}, 2] + {0, 0}, #] & /@ (* Trajectories built from *) Permutations[ (* All possible orderings of *) Join @@ ({{0, 1}, {1, 0}} & /@ Range[5]) (* Five steps N and five steps E*) ] )]  The RandomReal[{0,0.1},2] is a random near-the-origin starting location, just to offset the different lines from one another visually. You could try something like this: Show[Graphics[{RandomColor[], Line[#]}] & /@ ( (* Make graphics of *) FoldList[Plus, RandomReal[{0, 0.1}, 2] + {0, 0}, #] & /@ (* Trajectories built from *) Permutations[ (* All possible orderings of *) Join @@ ({{0, 1}, {1, 0}} & /@ Range[5]) (* Five steps N and five steps E*) ] )]  The RandomReal[{0,0.1},2] is a random near-the-origin starting location, just to offset the different lines from one another visually. 1 answered Apr 12 '16 at 1:49 evanb 3,4551212 silver badges2121 bronze badges You could try something like this: Show[Graphics[{RandomColor[], Line[#]}] & /@ ( (* Make graphics of *) FoldList[Plus, RandomReal[{0, 0.1}, 2] + {0, 0}, #] & /@ (* Trajectories built from *) Permutations[ (* All possible orderings of *) Join @@ ({{0, 1}, {1, 0}} & /@ Range[5]) (* Five steps N and five steps E*) ] )]  The RandomReal[{0,0.1},2] is a random near-the-origin starting location, just to offset the different lines from one another visually.