Exact Hausdorff and packing measures for random self-similar code-trees with necks

Random code-trees with necks were introduced recently to generalise the notion of $V$-variable and random homogeneous sets. While it is known that Hausdorff packing dimensions coincide irrespective overlaps, their exact measure has so far been largely ignored. In this article we consider general question an appropriate gauge function for positive finite measure. We first survey current state knowledge establish some bounds on these functions. then show self-similar do not admit a functions simultaneously give almost surely. This surprising result in stark contrast recursive model sheds light whether sets interpolate between conclude by discussing implications our results.