One rule at a time
Hold the number of turns steady, then change expansion. A larger W makes successive turns spread apart more quickly.
A SMALL MUSEUM OF GROWING FORMS / NO. 001
A little shell.
An unfolding universe.
Change a growth rule. Add a turn. Discover the geometry hidden in a shell.
FIG. 01 / LOGARITHMIC SPIRAL
r = aebθ
For this logarithmic spiral, b = ln(W)/(2π). Equal angular steps multiply the radius by a constant factor. The outer radius is normalized on screen.
Always golden?
Not every shell follows the golden ratio. This lab does not assume a golden spiral. A flat curve cannot describe the full geometry of a three-dimensional shell.
Field notes
Is this an actual snail shell?
It is a mathematical illustration with shell-inspired colors, not a species identification or husbandry diagnostic tool.
How does comparison work?
Pin the current curve, then change a slider. The green dashed curve preserves the previous shape at the same normalized scale.
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