# Angle increment spiral in Mathematica

What method cold I use to obtain a Plot similar to the one in the picture?

• Have you already tried to plot something yourself? Generally you’ll get more bites if you actually tried something...posting the code you used aswell is helpful. May 15 '19 at 17:41
• Related: Pentagonal spiral in Mathematica. The figure you are asking for is actually produced in the question text of Filling Space with Pursuit Polygons, although the question is not really about this figure. May 15 '19 at 17:45
• see also Drawing the Pursuit curves. May 15 '19 at 19:50

steps = Table[{r, 1.005 (2 Pi/4)}, {r, 1, 25, 0.2}];
Graphics[{Black, Line@AnglePath[steps]}, Background -> White]


The spiral tendency is controlled by the value 1.005 in the code, and the spacing between the lines is controlled by the value 0.2.

Not really an answer, since this isn't a single line but I thought it was interesting so I'll post it.

rc = Rectangle[];
center = {0.5, 0.5};
transforms = Table[
ScalingTransform[{x, x}, center] @* RotationTransform[(1 + -x) * Pi / 4, center],
{x, 1, 0.025, -0.025}
];
Graphics @ {EdgeForm @ Black, FaceForm @ None, GeometricTransformation[rc, transforms]}


Um, I like spirals. So as @C.E. points out, AnglePath is a useful function.

 Manipulate[
Graphics[{Thick,
MapIndexed[{ColorData[cs, (#2[[1]]*d)^e], Line[#]} &,
Partition[AnglePath[Table[{r, a*Degree}, {r, 0, 1., d}]], 2, 1]]
}, Background -> Black, ImageSize -> 500],
{{d, 0.01, "Step Increment"}, 0.002, 0.02, Appearance -> "Labeled"},
{{a, 119., "Angle Increment (Degree)"}, 1., 180., Appearance -> "Labeled"},
{{e, 1.5, "Colour Exponent"}, 0.1, 3.0, Appearance -> "Labeled"},