Systems, methods, and devices allow intravascular or percutaneous mapping, orientation or ablation, or combinations thereof in bodily cavities or lumens. A device includes a plurality of elongate members which are moveable between an unexpanded configuration, a bent or coiled stack configuration and an expanded or fanned configuration. The elongate members form a stack arrangement in the unexpanded configuration to fit through a catheter sheath. The elongate members follow respective arcuate or curvilinear paths as advanced from the sheath into the bent or coiled stack configuration, adopting volute, scroll or rho shapes, and may be nested. The elongated members are fanned or radially spaced circumferentially with respect to one another into the expanded or fanned configuration. Transducers carried by elongate members may sense various physiological characteristics of or proximate tissue, for instance temperature, and / or may apply energy to or proximate tissue, for example to perform ablation. The device is retractable.