### Post by ashrothedm on Jan 10, 2015 1:32:30 GMT

@dndpaladin

Grids have incremental polygonal boundaries, as do virtual grids. Moving to any possible location within your movement range is confined by the limited number of bounding polygons. There is a finite amount of space in a grid. If I have a move of 1, and I am in any shaped grid (which again requires non-overlapping boundaries), the number of locations that I could be would always be 1+sides. If it's triangular, 4. if it's rectangular, 5, hexagonal 7, etc. It's finite.

In gridless, if you were to draw a virtual grid of all possible movement locations within the move range in an open field using a blue pen, the "grid" would be a perfectly filled in large blue circle, as the grid lines infinitely and fractally overlapped. If I have a move of 1, I can go in any direction and at any distance less than or equal to 1.

No matter the grid you define virtually, you are not going to move 1/2". As soon as you do, you are not on a virtual grid, real grid, or otherwise. Your possible outcomes near infinity, and the greater the resolution of measured outcomes, the greater number of distances you can travel. it will follow a fractal and exponential increase as resolution increases.

You should look up the math regarding the measuring of coastlines with fractals. The most amazing thing, is that the more finite the measurement increments of a coast becomes, the longer it is. en.wikipedia.org/wiki/Coastline_paradox

Gridless, at best according to your description, is measured with fractals. As the measurement and size of the grid increments approaches 0, the possible outcomes of the "grid" approach infinity. In short, you're dividing the possible outcomes of movement by 0. 0 = gridless. gridless is infinite outcomes.

The pattern of my circle only uses one speed to illustrate that the grid is compromised immediately by the base, as each degree of movement overlaps the base, Try drawing it out as I described and track movement by degrees and distance. Then move again. It's not practical to consider a grid virtually. For facing and all of that other jazz, the "grid" that follows the player could just as well be directional arcs on their base.

Grids have incremental polygonal boundaries, as do virtual grids. Moving to any possible location within your movement range is confined by the limited number of bounding polygons. There is a finite amount of space in a grid. If I have a move of 1, and I am in any shaped grid (which again requires non-overlapping boundaries), the number of locations that I could be would always be 1+sides. If it's triangular, 4. if it's rectangular, 5, hexagonal 7, etc. It's finite.

In gridless, if you were to draw a virtual grid of all possible movement locations within the move range in an open field using a blue pen, the "grid" would be a perfectly filled in large blue circle, as the grid lines infinitely and fractally overlapped. If I have a move of 1, I can go in any direction and at any distance less than or equal to 1.

No matter the grid you define virtually, you are not going to move 1/2". As soon as you do, you are not on a virtual grid, real grid, or otherwise. Your possible outcomes near infinity, and the greater the resolution of measured outcomes, the greater number of distances you can travel. it will follow a fractal and exponential increase as resolution increases.

You should look up the math regarding the measuring of coastlines with fractals. The most amazing thing, is that the more finite the measurement increments of a coast becomes, the longer it is. en.wikipedia.org/wiki/Coastline_paradox

Gridless, at best according to your description, is measured with fractals. As the measurement and size of the grid increments approaches 0, the possible outcomes of the "grid" approach infinity. In short, you're dividing the possible outcomes of movement by 0. 0 = gridless. gridless is infinite outcomes.

The pattern of my circle only uses one speed to illustrate that the grid is compromised immediately by the base, as each degree of movement overlaps the base, Try drawing it out as I described and track movement by degrees and distance. Then move again. It's not practical to consider a grid virtually. For facing and all of that other jazz, the "grid" that follows the player could just as well be directional arcs on their base.