: ( div ) : ( div )draw set( ) (iuntil end hilbert fig hilbert curves similar but slightly more complex and aesthetically more sophisticated example is shown in fig this pattern is again obtained by superimposing several curvestwo of which are shown in fig si is called the sierpinski curve of order what is its recursion schemeone is tempted to single out the leaf as basic building blockpossibly with one edge left off but this does not lead to solution the principal difference between sierpinski curves and hilbert curves is that sierpinski curves are closed (without crossoversthis implies that the basic recursion scheme must be an open curve and that the four parts are connected by links not belonging to the recusion pattern itself indeedthese links consist of the four straight lines in the outermost four cornersdrawn with thicker lines in fig they may be regarded as belonging to non-empty initial curve which is square standing on one corner now the recursion schema is readily established the four constituent patterns are again denoted by abc and dand the connecting lines are drawn explicitly notice that the four recursion patterns are indeed identical except for degree rotations