Studies the fractal properties of shallow volcanic tremor and gas piston events associated with magma degassing at Kilauea Volcano, Hawaii, using data from two dense short-baseline arrays of seismographs deployed near the active crater of Puu Oo on the east rift of the volcano. The existence of a categorically stable attractor characterizing both types of activities strongly suggests that the excitation mechanism of tremor is similar to that of gas piston events, which in turn are correlated with visual observations at the volcanic vent. Low values derived for the dimension of the attractor in phase space points to significant self-organization in the process of generation of tremor and offers general constraints on the dimensionality of attractors derived from models of acoustic emission associated with magma flow, vesiculation, and degassing. -from Authors