The electric spatial pattern and invertase activity distribution in growing roots of azuki bean (Phaseolus chrysanthos) have been studied. The electric potential near the surface along the root showed a banding pattern with a spatial period of about 2 cm. It was found that the enzyme activity has a peak around 3-7 mm from the root tip, in good agreement with the position of the first peak of the electric potential, which is located a little behind the elongation zone. An inhomogeneous distribution of ATP content was also detected along the root. Experiments on the electric isolation of the elongation zone from the mature zone and acidification treatment showed that H+ is transported from the mature-side to elongation-side regions, causing tip elongation through an acid-growth mechanism. Both acidification and electric disturbance on growing roots affected growth significantly. Simultaneous measurements of electric potential and enzyme activity clearly showed a good correlation between these two quantities and growth speed. From an analogy with the Characean banding, the spatio-temporal organization via the cell membrane in electric potential and enzyme activity can be regarded as a dissipative structure arising far from equilibrium. These experimental results can be interpreted with a new mechanism that the dissipative structure is formed spontaneously along the whole root, accompanied by energy metabolism, to make H+ flow into the root tip.