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, which holds detail cleanly out to about 100,000× magnification. That covers every landmark on this page with room to spare — the kind of places you can actually sit and watch. The extreme million-times zooms you see in long-form videos fall outside that range and are rendered offline with arbitrary-precision engines, not live in a browser tab.
Where single-precision zoom actually breaks down (measured)
Most guides say GPU fractal renderers "run out of precision eventually" without saying where. We measured it. Rendering the seahorse-valley point at increasing magnification on a real WebGL2 GPU and counting the distinct shade transitions across a frame — a proxy for how much genuine structure survives — the image holds together to 100,000× and then falls off a cliff. At 100,000× a frame still resolved around 36,000 transitions. At 1,000,000× that collapsed to roughly 5,400: the same view, mostly flat blocks, because adjacent pixels no longer map to distinguishable points on the complex plane.
The second measurement was more surprising, and it changed how Vortexia works. Iteration count is usually treated as "more is better". It is not. At 100,000× magnification, 600 iterations resolved 119 distinct shades; 1,500 iterations resolved only 74. Past roughly 600 you are spending GPU time for a worse picture, because the extra iterations resolve detail finer than single-precision coordinates can distinguish, and the result aliases into noise. Vortexia therefore caps iteration depth at 600 and scales it with zoom automatically — raising magnification without raising iterations produces a flat grey blob, and raising it beyond 600 produces mush.
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.