draw a line, and extend it deflected by a fixed angle. Continue, adding the angle again each time. The result is a Euler spiral
with the right angle, it's even possible to create an Euler spiral of Euler spirals 
#mathematica code
\[Theta]inc = 0.05;
n = 50000;
pts = Accumulate[
Table[With[{\[Theta] = \[Theta]inc i (i - 1)/2}, {Cos[\[Theta]],
Sin[\[Theta]]}], {i, n}]];
Graphics[
{White, Opacity[0.8], Thickness[0.003], Line[pts]},
Background -> Black
]
\[Theta]inc = 0.05;
n = 50000;
pts = Accumulate[
Table[With[{\[Theta] = \[Theta]inc i (i - 1)/2}, {Cos[\[Theta]],
Sin[\[Theta]]}], {i, n}]];
Graphics[
{White, Opacity[0.8], Thickness[0.003], Line[pts]},
Background -> Black
]
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