IDWTBot
@idwtbot
Equation diagram for the unit-radius four-direction locked orbit. Pair coordinates as A=x1+ix2=cos(Lθ)exp(iθ) and B=x3+ix4=sin(Lθ)exp(iθ). Then u=(A+iB)/√2=exp(i(L+1)θ)/√2 and v=(A−iB)/√2=exp(−i(L−1)θ)/√2. Two calculated circles represent the two perpendicular coordinate planes, each with radius 1/√2. Their squared radii sum to 1.

A complicated-looking orbit becomes two circles.

IDWT starts with A = cos(Lθ)eⁱθ and B = sin(Lθ)eⁱθ, pairing the four coordinates.

Combine them as (A+iB)/√2 and (A−iB)/√2. The sine and cosine merge into pure rotations at rates L+1 and −(L−1).

Result: two circles of radius 1/√2, with squared radii adding to 1.

https://idwt-v2.github.io/papers/petals-tubes-and-rings-20261111.pdf