alt=A three-dimensional Mandelbox fractal of scale 2.|thumb|right|A "scale-2" Mandelbox alt=A three-dimensional Mandelbox fractal of scale 3.|thumb|right|A "scale-3" Mandelbox alt=A three-dimensional Mandelbox fractal of scale -1.5.|thumb|right|A "scale -1.5" Mandelbox In mathematics, the mandelbox is a fractal with a boxlike shape found by Tom Lowe in 2010. It is defined in a similar way to the famous Mandelbrot set as the values of a parameter such that the origin does not escape to infinity under iteration of certain geometrical transformations. The mandelbox is defined as a map of continuo
alt=A three-dimensional Mandelbox fractal of scale 2.|thumb|right|A "scale-2" Mandelbox alt=A three-dimensional Mandelbox fractal of scale 3.|thumb|right|A "scale-3" Mandelbox alt=A three-dimensional Mandelbox fractal of scale -1.5.|thumb|right|A "scale -1.5" Mandelbox In mathematics, the mandelbox is a fractal with a boxlike shape found by Tom Lowe in 2010. It is defined in a similar way to the famous Mandelbrot set as the values of a parameter such that the origin does not escape to infinity under iteration of certain geometrical transformations. The mandelbox is defined as a map of continuous Julia sets, but, unlike the Mandelbrot set, can be defined in any number of dimensions. It is typically drawn in three dimensions for illustrative purposes.
== Simple definition == The simple definition of the mandelbox is this: repeatedly transform a vector z, according to the following rules: First, for each component c of z (which corresponds to a dimension), if c is greater than 1, subtract it from 2; or if c is less than -1, subtract it from −2. Then, depending on the magnitude of the vector, change its magnitude using some fixed values and a specified scale factor.
Discovered by embedding cosine similarity (sentence-transformers MiniLM, 384-dim).