λ-Parameter Space (click to pick λ)
Dynamical Plane (Newton Basins)
Current λ
Re(λ): —
Im(λ): —
Seed z₀ = λ/3:
Re(z₀): —
Im(z₀): —
Basin Colors
Root r₁ = +1
Root r₂ = −1
Root r₃ = λ
λ-space: 2-cycle / no conv.
Key formula:
p(z) = (z+1)(z−1)(z−λ)
Newton step:
z → z − p(z)/p′(z)
Mandelbrot boundary:
|c| ≈ 1/4 (main cardioid)
Centroid λ/3 lies at
the Mandelbrot boundary
when λ traces the
cardioid of the M-set.
p(z) = (z+1)(z−1)(z−λ)
Newton step:
z → z − p(z)/p′(z)
Mandelbrot boundary:
|c| ≈ 1/4 (main cardioid)
Centroid λ/3 lies at
the Mandelbrot boundary
when λ traces the
cardioid of the M-set.