WHORLTay Glasshouse · Dundee
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An exhibition · Tay Glasshouse, Dundee

Every coiled shell is one curve, grown.

WHORL is a free exhibition about how shells grow. 14 November 2026 to 18 April 2027.

Scroll · 24 shells from Regenfuss's plates, 1758

Change one number:

W how fast it widens

D how far from the axis

T how far it slides

S the shape of the opening

From the nautilus at 3.15 to a scallop at 10¹⁴, one number decides how many turns a shell needs.

Hold the opening away from the axis and the coils open up, until they no longer touch at all.

At zero the shell stays flat; slide further with every turn and it climbs into a tower.

Round, a tall slit, a notch for the siphon: the same growth makes a cone, an olive or a whelk.

01 / 04

  1. 01 · Grow

    It starts as a speck.

    A shell begins as a tiny larval shell, the protoconch, and grows only at its opening. Here a periwinkle from the Tay shore adds its six turns; the old ones keep their shape inside the new.

  2. 02 · W widening

    Widen slowly, climb high.

    Lower W from 2.05 to 1.2 and each turn is barely wider than the last. To reach the same size the tube needs 23 turns instead of 6.

  3. 03 · D distance

    Leave a gap at the centre.

    Move the opening away from the coiling axis. At D 0.45 the turns stop touching and you can look down the middle.

  4. 04 · T travel

    Stop sliding, lie flat.

    Set T to zero and every turn stays in one plane. The periwinkle flattens into the coil of an ammonite.

  5. 05 · S shape

    Change the opening.

    Stretch the round opening into a tall slit, wider at the shoulder, and the same growth draws a slender cone.

  6. 06 · The paint

    The lip paints as it grows.

    Pigment cells along the lip each answer their neighbours, one row at a time. The textile cone's triangles match Rule 30: left XOR (centre OR right).

1966 · David Raup

Raup let a computer draw shells from these numbers.

Most of what it drew, no animal has ever grown.

Read the idea

Room 4 · The empty cube

Grown, and never grown.

Sharp: the twelve shells on show. Blurred: shells the model can draw from numbers outside the regions where real shells sit.

Point at a shell

What's on

Four rooms in the Glasshouse.

  1. Room 1

    The curve

    Dürer's eternal line, Bernoulli's marvellous spiral and the book D'Arcy Thompson wrote in Dundee.

  2. Room 2

    Four numbers

    Twelve shells, each beside the model that grows it from four numbers.

  3. Room 3

    The paint

    How the lip lays down a pattern row by row: the textile cone's triangles and the olive's tents.

  4. Room 4

    The empty cube

    The shells that four numbers can draw and no animal has grown.