The Mandelbrot set has famous landmarks the way a country has famous cities — specific coordinates that legendary zoom videos return to again and again. This guide lists the classic ones with their exact center coordinates, and every entry is a live link: click it and Vortexia opens a gently animating view centered right on that spot, running the real z → z² + c math on your GPU. No download, no account.
How to read the coordinates
Each landmark is given as a center point (cx, cy) on the complex plane and a zoom level. cx is the real (horizontal) part, cy is the imaginary (vertical) part, and higher zoom means you are magnified deeper into the boundary. Vortexia renders with single-precision GPU math, so these are all shallow, beautiful landmarks that stay crisp — the kind of places you can actually sit and watch, rather than the extreme million-times zooms that need special arbitrary-precision engines.
The classic Mandelbrot landmarks
Click any location to open it live:
- Home — the whole set · (−0.5, 0) — The full Mandelbrot set: the heart-shaped main cardioid, the period-2 bulb on its left, and the antenna reaching west. Start here.
- Seahorse Valley · (−0.745, 0.113) — The narrow pinch between the cardioid and the period-2 bulb. Its filaments curl into shapes that look unmistakably like seahorse tails.
- Elephant Valley · (0.2825, 0.01) — On the right-hand seam of the cardioid, a parade of spiral shapes marches along the edge like a line of elephants trunk-to-tail.
- Triple Spiral Valley · (−0.088, 0.654) — A famous stop from the classic zoom videos, where filaments wind into interlocking three-armed spirals.
- A mini-Mandelbrot · (−1.7685, 0.0005) — Out along the western antenna hides a tiny, near-perfect copy of the entire set — proof of the fractal's self-similarity.
- Scepter Valley · (−1.36, 0.005) — Along the western spike, delicate branching filaments fan out like ornate scepters.
Why some coordinates need higher iterations
The deeper you zoom, the more points sit right on the knife-edge of the boundary — and those points need more iterations of z → z² + c before you can tell whether they escape. That is why the valley links use 400–500 iterations while the home view only needs about 120. Too few iterations and fine filaments dissolve into black; enough iterations and the detail sharpens back up. It is the single most important setting when you explore.
Explore your own coordinates
Every Vortexia demo link is just a URL you can edit. Change cx and cy to recenter, raise zoom to magnify, bump iter for more detail, and set color (0–360) to recolor. For example, /demo?type=mandelbrot&cx=-0.75&cy=0.1&zoom=50&iter=450&color=180 drops you into a fresh corner of Seahorse Valley. Copy a link, tweak the numbers, and you have your own coordinate to share.