Aperiodically woven textile having a square starting pattern (Q) composed of two weft threads and two warp threads. A peripheral rotation point is fixed in the middle of one side, three copies of this starting pattern being rotated successively through 90°, 180° and 270° about said rotation point and positioned in a fan-like manner one behind another to obtain a composed pattern then fixed as the starting pattern (Q) for a corresponding following fan-like composition. This approach iteratively develops patterns of any desired size from crossing points of threads corresponding to the fabric. In the starting pattern (Q), one weft thread, as seen extending from left to right, first crosses over one of the warp threads and then crosses under the other, and the other weft thread crosses over both warp threads, where the threads aperiodically jump orthogonally over one to three threads in the fabric structure.