On Julia and Mandelbrot sets in double numbers plane
2010jmw | Tipunin I., Toporensky A.  // Lebedev Physical Institute, Moscow, Russia; Sternberg Astronomical Institute, Moscow, Russia atopor@rambler.ru

Mandelbrot set and filled-in Julia sets in double numbers plane have been found numerically. We discuss differences between our definition of these sets and the definition of Artzy. A condition for these two different types of sets to coincide have been found. We show also that our definition allows graphycally interesting escaping time diagramms to be constructed in the double numbers plane, in contrast to the Artzys definition.

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