A Mandelbrot set for pairs of linear maps
The set of points \(A(s)=\{\pm 1\pm s\pm s^ 2\pm s^ 3\pm..\). for all sequences of \(+\) and -\(\}\), where \(s\in {\mathbb{C}}\) and \(| s| <1\), is generically a fractal. For example A(1/3) is the classical Cantor set and \(A(1/2+i/2)\) is a dragon curve. This set of fractals can be classified in terms of an associated Mandelbrod set \(D=\{s\in {\mathbb{C}}:\) \(| s| <1\), A(s) is disconnected\(\}\). The structure of D and its boundary are investigated.
scientific article; zbMATH DE number 3932054