> you cannot break a hexagon into smaller hexagons
Actually you can.
1. Think of hexagons as six equilateral triangles sharing a center point.
2. Place one smaller vertically flipped equilateral triangle, in each original triangle.
3. Each original hexagon center point is now the center of a smaller (1/2 linear dimension, 1/4 area) hexagon.
4. New small hexagons replace each of the six original hexagon's edges. Since edges are shared, this is an increase a 3x increase in number of hexagons.
So each new hexagon has 1/4 the area of the original ones (and 1/2 the linear dimensions). This results in 2x the linear dimension resolution, 4x the area resolution.
Grids could also be increased in scale the same way. By retaining a half-sized (in linear terms) square at the center of each original square, and turning each original edge and corner into new squares. With the same 1/2 and 1/4 ratios of linear and area scaling.
Actually you can.
1. Think of hexagons as six equilateral triangles sharing a center point.
2. Place one smaller vertically flipped equilateral triangle, in each original triangle.
3. Each original hexagon center point is now the center of a smaller (1/2 linear dimension, 1/4 area) hexagon.
4. New small hexagons replace each of the six original hexagon's edges. Since edges are shared, this is an increase a 3x increase in number of hexagons.
So each new hexagon has 1/4 the area of the original ones (and 1/2 the linear dimensions). This results in 2x the linear dimension resolution, 4x the area resolution.
Grids could also be increased in scale the same way. By retaining a half-sized (in linear terms) square at the center of each original square, and turning each original edge and corner into new squares. With the same 1/2 and 1/4 ratios of linear and area scaling.