Dynamic touching is effortful touching. It entails deformation of muscles and fascia and activation of the embedded mechanoreceptors, as when an object is supported and moved by the body. It is realized as exploratory activities that can vary widely in spatial and temporal extents (a momentary heft, an extended walk). Research has revealed the potential of dynamic touching for obtaining non-visual information about the body (e.g. limb orientation), attachments to the body (e.g. an object's height and width) and the relation of the body both to attachments (e.g. hand's location on a grasped object) and surrounding surfaces (e.g. places and their distances). Invariants over the exploratory activity (e.g. moments of a wielded object's mass distribution) seem to ground this ‘information about’. The conception of a haptic medium as a nested tensegrity structure has been proposed to express the obtained information realized by myofascia deformation, by its invariants and transformations. The tensegrity proposal rationalizes the relative indifference of dynamic touch to the site of mechanical contact (hand, foot, torso or probe) and the overtness of exploratory activity. It also provides a framework for dynamic touching's fractal nature, and the finding that its degree of fractality may matter to its accomplishments.