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Binets Formula Spiral

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Spiral convolution of Binet curve

Fig. 1 Binet's curve produced by Binet's formula. The spiral and ovals cross at the Fibonacci numbers.

A swirling graphic is produced when the curve of Binet's Formula is rotated about the axis as a function of the index value along the axis.

Per each sinusoidal π cycle, a multiplier of π radians on the angle of rotation produces a beautiful alignment of two spirals in 3D.

Orthographic 2D projections

Fig. 2. A 2D projection through a spiral vortex pair made with Binet's Formula rotated in 3D by θπ radians. © DonEMitchell

The view illustrated in Fig. 2 is straight down into the page from the negative X axis. The image was create in POVRay with an orthogonalized view (no perspective). The X-crossings on the vertical axis through the spiral center (origin) cross at Fibonacci numbers.

Four symmetries mirrored in the Y, anti-mirrored in the X