Three-dimensional recurring patterns in excitable media

A new method to create three-dimensional periodic patterns in excitable media is presented. The method is demonstrated and the patterns are obtained with the help of two types of 3D “spiral pairs” generators, which are respectively based on a “corner effect” and a “unidirectional propagation” processes. The results portray time-repeating patterns resembling fruits or potteries. The method is easy to implement and can be used to form other types of 3D patterns in excitable media. The question of periodicity of the patterns thus obtained is resolved by calculating the singular lines (filaments) around which they evolve and showing their unique reattachment property. Actual realizations could be conceived e.g. in chemical reactions such as Belousov–Zhabotinsky. Possible severe cardiac arrhythmias following the appearance of such patterns in the action potential of the heart are considered.

► New method to create three-dimensional periodic patterns in excitable media.
► Singular lines (filaments) for the corner effect are presented.
► Filaments are shown to exhibit periodic behavior.