Adaptive random testing (ART) is an enhanced version of random testing (RT). It has been observed that the compactness of failure regions is one of the factors that affect the performance of ART. However, this relationship has only been verified with rectangular failure regions. This paper further investigates the relationship between the compactness of failure regions and the performance of ART by conducting simulation experiments,where various regular and irregular failure regions are studied. The experimental results have shown that ART's performance improves as the compactness of failure regions increases. This study has provided further insights into the conditions where ART outperforms RT.