#### Topic: Algorithm of generation of one-dimensional patterns

Colleagues, and whether exist methods for the decision of the following task. There is some area of space. It is broken into cells (the nearest analogy the image broken into pixels). There is some curve f (x, y) = (x (t), y (t)) if it transits through a cell the cell is considered painted over. It is necessary to pick up such curve that it painted over the maximum number of cells but satisfied to following conditions 1. Absence of self-intersections. The curve should not transit through the same cell twice 2. Sufficient smoothness (max_t (dx (t)/dt) ^2 + (dy (t)/dy) ^2 <T) 3. Uniqueness of a pattern - in any area in the size MxN the pattern should be unique. (I.e. if to linearize this area and to transform into binary number) that numbers on all image will not repeat.