I will be considering these two formulas which are good for modelling a situation when you know the angle you want the plot to go in with respect to the x axis from a point and how far in that direction for each of n discrete steps...

With the meaning that X(n), Y(n) is the nth point in a series...And to show with an example first let L(i) = i and theta(i) = i*2*pi/5

Interestingly Maple knew the closed form, but it's not necessary for a limited number of points, it does make it easy to plug in any value of n and find the point without knowing any of the previous points though...

And we can make a list over n=1, 2, 3,4,5

And we can let the initial point be [0,0] to get:

An then plotting the above, both with natural number n and continuous n:In general L(i) can be any discrete function of length of lines for the plot and theta(i) can be any function for the angle the lines make with the x axis...

**Next is to see what happens when L(i) is a constant with a delta->0 length and theta(i) gets more continuous

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