M-Set

However, it contains only the briefest references to the M-Set, the exploration of which was barely beginning in 1982.

The Ghost from the Grand Banks Clarke, Arthur C. 1990

No one said a word until they were back at the original complete M-Set, now an ominous black fringed with a narrow border of golden fire, and shooting off jagged lightnings of blues and purples.

The Ghost from the Grand Banks Clarke, Arthur C. 1990

The boundary - if one can call it that - of the M-Set is not a simple line; it is something which Euclid never imagined, and for which there is no word in ordinary language.

The Ghost from the Grand Banks Clarke, Arthur C. 1990

However, even the first two or three terms are quite enough to show that the M-Set must have a very different shape from the perfectly circular S-set.

The Ghost from the Grand Banks Clarke, Arthur C. 1990

A point at that same distance may be outside the boundary of the M-Set.

The Ghost from the Grand Banks Clarke, Arthur C. 1990

One of the many strange thoughts that the M-Set generates is this.

The Ghost from the Grand Banks Clarke, Arthur C. 1990

Ever since the M-Set was discovered in 1980, people have managed to become obsessed with it.

The Ghost from the Grand Banks Clarke, Arthur C. 1990

The psychological reasons for this appeal are still a mystery, and may always remain so; perhaps there is some structure, if one can use that term, in the human mind that resonates to the patterns in the M-Set.

The Ghost from the Grand Banks Clarke, Arthur C. 1990

It's called the Mandelbrot Set (from now on, the M-Set) and you're soon going to meet it everywhere - in the design of fabrics, wallpaper, jewelry, and linoleum.

The Ghost from the Grand Banks Clarke, Arthur C. 1990

When we come on to the more complicated case of the M-Set, where the bearing is important, there's a very neat mathematical trick which takes care of it, by using complex or imaginary numbers (which really aren't at all complex, still less imaginary).

The Ghost from the Grand Banks Clarke, Arthur C. 1990