plotting - Turning a set of random walk data 45 degrees

I have a set of data that is just a "random" (generated by me, not by computer) sequence of length 2000 of 1's and (-1)'s. I used it to plot a 1-D random walk where +1 is step up, (-1) is step down, so my graph looked like this: enter image description here

I was asked to break the sequence in half and plot the first half against the second to create a 2-D random walk graph. This was easy enough, I just did it in excel. enter image description here

But I was then asked to turn the graph 45 degrees CCW so it looks like it's laid over a grid. So i guess if the first point is (1,1) it would go to (0,1), if it's (-1,1) it would go to (-1,0) and so on. I'm not sure how to do that. Please let me know if you know of a way to do it in Excel or Mathematica.

Answer

ListLinePlot[Accumulate @ Prepend[RandomChoice[{{-1, 0}, {1, 0}, {0, -1}, {0, 1}}, 1000], 
  {1, 1}], AspectRatio -> Automatic]

Starting with some random data

rd = RandomChoice[{1, -1}, 2000];

ListLinePlot[Accumulate@rd]

Creating a random walk similar to the one shown in your question

rw = Accumulate@Transpose[{rd[[;; 1000]], rd[[1001 ;;]]}];

ListLinePlot[rw, AspectRatio -> Automatic]

and rotating it by 45°

rwr = rw.(RotationMatrix[45 Degree]/Sqrt[2]);


ListLinePlot[rwr, AspectRatio -> Automatic]

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