#### What is the Mandelbrot Set?

The Mandelbrot set is a mathematical set of points that are computed from a relatively simple formula.

Its name comes from the Mathematician Benoit Mandelbrot who did not discover it but was one of the first to study it.

The Mandelbrot Set holds a special place among fractals as it is one of the more easily recognizable ones, while at the same time being very varied.

#### What makes this Fractal Exlorer different?

Typical fractal explorers compute the fractal on your machine, this means that exploration is slow, power-hungry or has to be compromised on quality.

The fractal here has been pre-computed to a high resolution:

• Exploration is fast and doesn't need much computing powre (or bandwidth)
• The Mandelbrot Set could be computed with a high number of iterations.
The Mandelbrot Set reveals itself more with high number of iterations, but more iterations mean more CPU time. Many areas of the fractal you can explore interactively actually took several minutes of computing time on fast CPUs.

#### This is a fractal, how many images are actually similar?

None! The Mandelbrot Set is only semi self-similar, which means that while you may recognize some patterns, they will never repeat in the exact same way.

There is one symmetry along the vertical axis, which was taken advantage of during the computation.

#### How many iterations were used?

The current database was computed on the smoothed Mandelbrot Set up to a depth of 65535.

It is likely that at some point in the future, relevant tiles could be recomputed to greater depth.

#### What are the (zoom) levels? How big is the image?

Each zoom level corresponds to a doubling of the resolution:
• Level 0 is made of a single 256x256 tile
• Level 1 is made of 2x2 = 4 tiles of 256x256 pixels
• Level 2 is made of 4x4 = 16 tiles of 256x256 pixels
• etc.
• Level 13, the current limit is made of 8192 tiles of 256x256 pixels
At Level 13, the whole image is thus made of 2097152x2097152 pixels, or 4 Tera Pixels, that is 4 millions of millions of pixels.

#### How large is the database?

The database for Level 13 is currently 32 GB in size (uncompressed it would be 8 TB).
The compression ratio is achieved by:
• taking advantage of the Y symmetry
• handling tiles of uniform depth specifically
• using ZLib highest compression

#### When will Level 14 or 15 be added?

At the moment there are no plans to add them, as the VM that hosts this site is out of storage space :-).
Even with all the compression, Level 14 is expected to be around 128 GB, and Level 15 would likely be breaching the half-Terabyte.