| Ultrasound transducers designed for therapeutic purposes such as tissue ablation or drug delivery require large apertures for adequate spatial localization while providing sufficient power. To this end, an array that is both space-filling and aperiodic in the placement of the elements was designed using the mathematical concept of aperiodic tiling. This design leads to reduced grating lobes while maintaining full surface area coverage to deliver maximum power. For illustration, a flat 2D array with 255 elements with two shapes was designed based on Penrose tiling to cover an aperture 4 cm x 4 cm with no sparseness while guaranteeing aperiodicity. The beam patterns (1.2 MHz tone burst of 8 ƒ8¡6s duration) from the array were simulated using the FIELD II program for multiple focal spots in a plane 6 cm from and parallel to the aperture. For comparison, beam patterns for the same excitation intensity from other 2D arrays with varying levels of regularity and sparseness were also computed: Periodic array, semi-periodic array, array with maximally packed circular elements, and random array with circular elements. The worst relative grating lobe level among all the focal spots were -2.5 dB (periodic and semi-periodic), -4.8 dB (maximally packed circles), -11.4 dB (Penrose), and -14.9 dB (sparse random circles). Both the Penrose and random arrays had beam patterns with commonly accepted grating lobe levels for therapeutic use of -10 dB or lower. The main lobe intensity was 71% higher for the Penrose array when the beam was focused on axis due to the full area usage compared to the random array. The grating lobe levels among sixteen off-axis focal spots were -12.06 dB ¡À 0.46 dB, with the best and worst being -12.9 dB and -11.4 dB respectively, indicating that the Penrose array had no directional preference. This work demonstrates that the concept of space-filling aperiodic tiling can be used to generate therapy arrays that are able to provide higher power for the same total transducer area compared to fully random arrays while maintaining acceptable grating lobe levels. |