A catheter has a mapping assembly having a plurality of splines mounted at its distal portion. The splines each have a proximal end disposed at the distal portion of the catheter body and a distal end and configured as a Fibonacci spiral arm that diverges outwardly from the proximal end. The splines have a support arm with shape memory, a non-conductive covering in surrounding relation to the support arm, at least one location sensor mounted at or near the distal end, a plurality of electrodes mounted in surrounding relation to the non-conductive covering, and a plurality of electrode lead wires extending within the non-conductive covering. Each electrode lead wire is attached to a corresponding one of the electrodes.