3 problems

Let $\alpha$ satisfy … where $\tau$ is the golden ratio, and let $\gamma$ denote the tilt angle of the growth form of the hat tiling. Hat growth-form tilt conjecture. The growth fo…

For positive $b\neq 1$, let $Tile(1,b)$ be the deformed hat tile, and let a tiling by these tiles have growth form with area $area_{growth\ form}$. The tile has area…

An L-tetromino tiling is a tiling by L-shaped tetrominoes, and its growth form is the asymptotic shape obtained from its coordination shells. L-tetromino nonpolygonality conjecture…