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A conformal pinning array can be created by conformally transforming a uniform triangular pinning lattice to produce a new structure in which the six-fold ordering of the original lattice is conserved but where there is a spatial gradient in the density of pinning sites. Here we examine several aspects of vortices interacting with conformal pinning arrays and how they can be used to create a flux flow diode effect for driving vortices in different directions across the arrays. Under the application of an ac drive, a pronounced vortex ratchet effect occurs where the vortices flow in the easy direction of the array asymmetry. When the ac drive is applied perpendicular to the asymmetry direction of the array, it is possible to realize a transverse vortex ratchet effect where there is a generation of a dc flow of vortices perpendicular to the ac drive due to the creation of a noise correlation ratchet by the plastic motion of the vortices. We also examine vortex transport in experiments and compare the pinning effectiveness of conformal arrays to uniform triangular pinning arrays. We find that a triangular array generally pins the vortices more effectively at the first matching field and below, while the conformal array is more effective at higher fields where interstitial vortex flow occurs. [ABSTRACT FROM AUTHOR]