[en] We present a model of gravity in which the Planck mass is generated spontaneously by a similar mechanism that is responsible for the tension in a recent membrane model of strings. The action describes very floppy fluctuations of the physical space in some large flat embedding space. The coupling constant is dimensionless but the fluctuations are so violent that they produce spontaneously a mass which plays the role of the dimensionally transmuted coupling constant and can be identified with the Planck mass. (orig.)