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In this manuscript we study single-line approximations and fractals based onthe Apollonian gasket. The well-known Apollonian gasket is the limit case ofconfigurations of kissing circles. Rather than plotting the circles as discs ona differently colored background (the traditional representation), we draw allcircles as one line without lifting the pen and without crossing itself.Moreover, the configurations are nested. In this manuscript we explore whetherthe limit of the line drawings gives rise to a space filling fractal curve.

Single line Apollonian gaskets: is the limit a space filling fractal curve?