The concept and automatic generation of the Curved Nonogram puzzle

In this paper we introduce a variation on the Nonogram puzzle that we call the Curved Nonogram. The rules for colouring are similar, but instead of being constrained to a grid it is structured by arbitrary curves that can take any shape. This allows for puzzles that feel more unique and can have more beautiful images hidden in them. Together with the introduction of this new puzzle, we define classes of solvability for it and provide measurements to judge its aesthetics. We also propose an algorithm that can generate these Curved Nonograms, taking the desired solution image as input. We test this algorithm on 16 varied input images and find that all of the outputs have a unique solution - an important requirement for puzzle-book puzzles, and at least 10 of them satisfy the aesthetic criteria sufficiently that they could be used in a puzzle book