  The concept of derivative coordinate functions proved useful in the
formulation of analytic fractal functions to represent smooth symmetric binary
fractal trees [1]. In this paper we introduce a new geometry that defines the
fractal space around these fractal trees. We present the canonical and
degenerate form of this fractal space and extend the fractal geometrical space
to R3 specifically and Rn by a recurrence relation. We also discuss the usage
of such fractal geometry.
