Generated directly from the same escape-time and palette math described in The Mathematics — not screenshots, but the identical formulas standing in for the app's own output. Click any tile for the full-resolution render.

The Mandelbrot Set

Named, documented locations — plus a few found by exploring the boundary directly.

c full viewThe whole set at a glance

c ≈ −0.745 + 0.113iSeahorse Valley

c ≈ 0.275 + 0.007iElephant Valley

c ≈ −0.088 + 0.654iTriple Spiral Valley

≈20× deeperSeahorse Valley, deep spiral

c ≈ −1.861A satellite "baby Mandelbrot"

c = −1 at centerCardioid / period-2 junction

c ≈ −1.401Period-doubling cascade

toward c = −2The main antenna

≈3,000× deeper stillA deep double spiral

Julia Sets

Six among the most famous named examples in complex dynamics, plus four supporting ones.

c ≈ −0.123 + 0.745iDouady's Rabbit

c = −1 exactlySan Marco / Basilica

c = 0.25 exactlyCauliflower

c ≈ −0.3905 + 0.5868iSiegel Disk

c ≈ −1.7549Airplane

c = i exactlyDendrite

c ≈ −0.745 + 0.113iSeahorse Valley, as a Julia parameter

c = 0.6 + 0.4iFatou dust

c = −0.8 + 0.156iA dragon-like spiral

c = −1.25Dendritic filaments

On Apple TV

A different kind of gallery entry — actual screenshots this time, not formula renders. Submitted for App Store review: an ambient, hands-free tour built for the big screen.

The full set, ambient and hands-free

AUTO drifts deeper on its own

A live Fractint palette, fetched at random

One remote button swaps to Julia

Put it on and watch

On Apple Vision Pro

Real screenshots again — the Mandelbrot set as an object in the room, not a render on a screen.

A window in your room, any wall, any size

Julia opens as its own floating window

Palettes and Control float independently too

A built-in guide, right there with you