SPACE--FILLING CURVES GENERATED BY FRACTAL INTERPOLATION FUNCTIONS V. DRAKOPOULOS Department of Informatics, Theoretical Informatics, University of Athens, Panepistimioupolis, 157 71, Athens, Greece L. DALLA Department of Mathematics, University of Athens, Panepistimioupolis, 157 71, Athens, Greece Interpolation formulas are the starting points in the derivations of many methods in several areas of Numerical Analysis. The goal is always the same: to represent the data by a classical geometrical entity. Fractal interpolation functions provide a new means for fitting experimental data and their graphs can be used to approximate natural scenes. We show how one can construct space-filling curves using linear fractal interpolation functions. These curves result from the projection of the attractor of an iterated function system