# Angle increment spiral in Mathematica What method cold I use to obtain a Plot similar to the one in the picture?

## 3 Answers

Here is an adaptation of my answer here:

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[]*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"},
{{cs, "SandyTerrain", "Colour Scheme"}, ColorData["Gradients"]}
] • There is an interesting optical illusion when scrolling this figure up and down quickly! – Gustavo Delfino May 17 at 2:34