I like games or puzzles that create something while being played. Here is a simple example which I call Unbalance. The single player version is played on a rectangular grid, like this one:
A move consists of drawing a horizontal or vertical line segment of length 5 on the grid and within the box.
The first line segment can be placed arbitarily. All subsequent segments must cross exactly one already
drawn segment. Only two types of intersections between two segments allowed: They either
both divide each other both in the proportion 1:4 or both in the proportion 2:3. Contacts at an end point are
The last intersection not allowed because the vertical segment divides the horizontal segment in the proportion 2:3, while the horizontal segment divides the vertical segment in the proportion 1:4.
The goal is to place as many segments as possible without violating the rules. Here is an example with 11 segments.
The are many variations. For instance, you can play with red and blue segments. Here it is required that segments of the same color divide each other in the same proportion, while segments of different color divide each other in different proportions.
For several players, you can start on a larger board, and each player uses their own color. The last player who can still make a move wins the game, following the rules with different colors otherwise.