An introductory article on building fractal square-grid designs from the Morse-Thue sequence, for quilts, mosaics, counted-thread embroidery, and other grid-based decoration. It explains two substitution rules (Light and Dark) and applies them step by step to generate the L- and D-Generation patterns, showing that the two families are negatives of each other. It then gives a recursive formulation and shows Generations 5 and 6 of both families. Part 2 is announced to cover patterns with more than two colors.