3 min read
Every point in a fractal viewer is a specific location in the complex plane. If someone shares Mandelbrot coordinates with you, these are the numbers that tell you exactly where to reopen the view and how deep the zoom already is.
A fractal location is defined by four values:
is the real part of the complex number. It moves you left (negative) or right (positive).
is the imaginary part. It moves you down (negative) or up (positive).
The main Mandelbrot set fits roughly in the range x: −2.5 to 1, y: −1.25 to 1.25. Coordinates outside this range are mostly empty space.
determines how magnified the view is. A zoom of 1 shows the entire set. A zoom of 50,000 shows a region 50,000 times smaller.
Higher zoom requires higher iteration counts to resolve the fine detail. At extreme zoom levels (millions or billions), you need thousands of iterations.
(the "escape limit") controls how many times the formula is applied before declaring a point "inside" the set. More iterations reveal finer detail, at the cost of render time.
At low zoom, 256 iterations is usually enough. For deep zooms, you may need 1000–2000 or more.
FractalSet encodes all four values into the viewer URL. Copy the URL and anyone can open your exact view:
At normal zoom levels, the visible location can be reconstructed from the four main values above. At very deep Mandelbrot zooms, tiny rounding errors matter, so FractalSet keeps the exact viewer payload in the URL as well. That is what makes extremely deep saved coordinates reopen reliably instead of drifting to a nearby spot.
If you want examples of coordinates that are already worth reopening, use the zoom-location collection below rather than copying random numbers from screenshots.
