The Pelta and Game Mechanics

“Games are generally played on continuous fields. The placement of pieces is considered generic, which allows simple rules to interact with simple geometry to provide a basis for organization of the pieces and flow the game. Complex placement games include complex node-connections like Risk or linear games like backgammon or looping games like Monopoly.

The virtue of continuous field games is that they have a built in tree structure of choices. When you play chess or checkers, any rule you define for a piece’s movement is true for any portion of the game board. This built in diversity of choice can help carry a simple ruleset but also add depth to an elegant ruleset. It’s very easy, when building a linear or looping game, to remove the element of player choice to the point that all that gets measured is mistakes or inattention. One of the virtues of Poker as a strategy game is that the potential ‘next game state’ is very broad, though it is too broad, generally, to represent in a continuous field, and subject to a lot of chance. By placing your game on a continuous field of some kind, you include the idea of anticipating consequences, but with the virtue of being generic, so that any strategy you develop is valid in any situation, and doesn’t have to rest on the vagaries of luck (at least with respect to the branching choices inherent in the continuous field).

The physics analogy is that the universe is much the same when viewed in any direction, but the local differences are fascinating (for instance: earth; nice beaches).

The limitations of continuous fields is that they must exist (generally) in a 2 dimensional geometric plane. That means you can have equilateral triangles, squares, or hexagons, if you want to use basic reproducible tessellations. With snowflake designs, it’s possible to get more complicated than this, but ultimately, it will be a specific (predictable or random) pattern reproduced in a hexagonal or rectangular field.

The Pelta is based on a series of overlapping circles, which indicates a new way to think of continuous branching designs.pelta changes games

Variations on the Pelta

In a field of 3 sided objects, there is no overlap. That’s where we get hexes–they’re just 6 triangles. In a field of 4 sided objects, there aren’t any overlaps, either, though, by offsetting the squares, and placing a dot in the center, you can effectively reproduce the Hex as a continuous field game-board. 3 * 2 is 6, which is interesting but I don’t know what it means.

In any case, when you pass 4 sides, if you want to create a continuous field, you need to add more dimensions or allow overlap (basically the same thing). Pentagons will not fit together. But if you force them to overlap, and position them like triangles, then you have a series of sharp diamond shapes. It’s similar for every other shape. More and more splintered and fractured geometric shapes are created.

But circles have a special property, in that they have an infinite number of angles as points of intersection; and minimal surface area.

Peltas are the ultimate continuous game board. If you want more details, you can triple the density of the regular circles and mark their overlaps. Games are stuck, currently, in a paradigm of borders. When, in reality, any meaningful game-concept really revolves around a locus and connections. The locus of offset squares is the same as the locus of a hex-field.

In a field of overlapping circles, the set of loci and paths is far far larger than the basic geometric shapes. You can create a game with the arbitrary connections of Risk and the open endedness of poker with these shapes–but presented in a way where you don’t have to teach people how the loci connect. It’s built into the pattern how things will relate, and that means you can either make an otherwise complicated game elegant, or make an elegant game complicated.”

-Samuel Kite

December, 2016

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