Vogel Spiral

Author

Eric W. Weisstein
September 1, 2026

This notebook downloaded from https://mathworld.wolfram.com/notebooks/PlaneCurves/VogelSpiral.nb.

For more information, see Eric's MathWorld entry https://mathworld.wolfram.com/VogelSpiral.html.

©2026 Wolfram Research, Inc. except for portions noted otherwise

Figure

A Vogel spiral with 1000 points and divergence angle equal to the golden angle.

Module[{angle, points},
    angle = Pi (3 - Sqrt[5]);
    points = Table[
        Sqrt[n] {Cos[n angle], Sin[n angle]},
        {n, 0, 999}
    ];
    Graphics[{
        LightDarkSwitched[Black, White],
        PointSize[0.008],
        Point[points]
    }]
]