Logarithmic Shell

Fine ribs follow an expanding spiral tube. Exponential growth draws a sculptural shell from a compact mathematical rule.

Logarithmic Shell: Fine ribs follow an expanding spiral tube. Exponential growth draws a sculptural shell from a compact mathematical rule.Logarithmic Shell: Fine ribs follow an expanding spiral tube. Exponential growth draws a sculptural shell from a compact mathematical rule.

About this shape

Jacob Bernoulli's spira mirabilis · expanding tube

Logarithmic Shell, logarithmic spiral, drawn by GART: Fine ribs follow an expanding spiral tube. Exponential growth draws a sculptural shell from a compact mathematical rule.
Logarithmic Shell · CC BY 4.0

An original parametric line study. Density controls the number of traces, form changes their geometry, and turn and tilt choose the projection. Motion follows a closed twenty-four-second cycle; the selected frame is preserved in saved drawings and exports.

Behind the mathematics

Jacob Bernoulli1655–1705

The logarithmic spiral

Swiss mathematician so taken with the logarithmic spiral, which keeps its shape as it grows, that he called it spira mirabilis and asked for it on his tombstone.