Samaga, Hans-Joachim On fractal structures in circle geometries. (Über fraktale Strukturen in Kreisgeometrien.) (German) Zbl 0870.58070 Mitt. Math. Ges. Hamb. 14, 121-131 (1995). The author introduces and studies analogues of the classical fractal sets (Mandelbrot set and Julia sets) in the Minkowski and Laguerre planes. These constructions can be obtained if the standard multiplication of complex numbers is replaced by other operations obtained if \(j^2=1\) (the Minkowski plane) and \(j^2=0\) (the Laguerre plane) instead of \(j^2= -1\). Reviewer: I.S.Molchanov (Glasgow) MSC: 37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior 51B15 Laguerre geometries 51B20 Minkowski geometries in nonlinear incidence geometry 28A80 Fractals Keywords:Laguerre plane; Minkowski plane; Mandelbrot set; fractal sets; Julia sets PDFBibTeX XMLCite \textit{H.-J. Samaga}, Mitt. Math. Ges. Hamb. 14, 121--131 (1995; Zbl 0870.58070)