Home Explore Library Help

Search the archive⌘K

A living room for X videos. Grab, watch, keep.

PRODUCT

Explore
Library
Settings

LEARN

Field notes
Help & FAQ

LEGAL

Terms of Use
Privacy Policy
Report content

© 2026 XDL · Built for the den

Hilbert Curve, one path, refined six times, until it fills the whole square. · XDL

Home
Explore
Hilbert Curve, one path, refined six times, unti…

Hilbert Curve, one path, refined six times, until it fills the whole square.

@matharium

1 grabs

Up next

TUNED TO THIS CLIP

One hundred sixty points equally spaced on a circle carry the residues modulo 160, and from each residue k a straight chord runs to mk reduced modulo 160. Not one chord is curved, yet the family is tangent to a single curve. For whole m that envelope is an epicycloid of m − 1

A point runs once round a closed curve every period T, and its height y(t) is set against time, unrolling the curve into a wave. The circle gives sin θ. The astroid gives sin³θ = (3 sin θ − sin 3θ)/4, and the Gerono lemniscate y = sin θ cos θ gives ½ sin 2θ, an octave up. The

Walk near the edge of a Mobius strip. One lap puts you on the other face; two laps bring you home. It has only one side.

Hₓ(s) = diag(s, 1, 1) stretches space along x by the factor s and leaves the plane x = 0 fixed. Its determinant is s, the signed volume of the unit cube's image. At s = 0 the cube is crushed flat onto the plane; at s = −1 the map is the reflection I − 2nnᵀ, with H² = I and

The point e^(iθ) = cos θ + i sin θ, carried along a third axis by θ itself, winds a helix of radius 1 that makes one full turn every 2π. Seen down the θ axis the helix is the unit circle. Seen from the side its height is the real part, cos θ. Rolled a quarter turn about the

Each curve starts as a plus sign, and each step replaces every segment with a bent copy of itself. The Lévy C curve bends each segment into two at 45°, always to one side; the dragon alternates sides; the twindragon is a dragon closed by its own half turn. The terdragon follows

A Lissajous figure is the path traced by x = sin(at + δ) against y = sin(bt), two perpendicular oscillations and nothing more. Here a runs across and b runs down, forty nine cells driven by one shared phase δ. The path closes after finite time exactly when a : b is rational, and

Add the odd numbers one at a time: 1, 3, 5, 7, 9, 11. You always get a square.

No comments yet

Write a comment

Sign in with X to post

Say something. You’re first.