OBSERVATION CONTRACT
A recursive shape, not a material demo
This field shows the Sierpiński tetrahedron as a geometric construction. The visible gaps are part of the rule; no visitor is measured or ranked.
OBSERVATION CHAMBER / ACTIVE
Sierpiński Tetrahedron Observatory
Observe a tetrahedron that keeps the same shape while its scale and volume shrink.
geometry / fractal volume
Observation Model
RECURSIVE GEOMETRY
One form, four smaller copies
Open the tetrahedron and watch the same scale rule return at every generation.
3D view unavailable
The measured recursion still appears below. Use a browser with WebGL to inspect the solid.
Drag the field to rotate. The gaps are the removed middle tetrahedra, not a glass effect.
The field is ready. Depth 0 contains one tetrahedron.
- Generation
- 0
- Copies N = 4d
- 1
- Scale = 2−d
- 1
- Volume fraction
- 1
WHAT TO WATCH
Four copies keep the same proportion
- At every new generation, each copy has half the edge scale.
- The copy count grows as
N = 4d, while the remaining volume halves. - With
d = 5, 1,024 small tetrahedra remain separated by gaps.
MODEL NOTE
Self-similarity fixes the dimension
N = 4 copies, each with scale s = 1/2; remaining volume V/V0 = (1/2)d.
D = log 4 / log 2 = 2. The value describes the scaling rule of this set, not the surrounding 3D space.
OBSERVATION POLICY
This chamber runs a browser-local Sierpiński tetrahedron model with a fixed recursion rule. Geometry, calculations, and images are not uploaded. It does not measure people, ability, health, or rankings.
Route
This chamber belongs to Shape & Space.
GEOMETRY Back to Shape & Space Route.