Seed Patterns

Introduction

A seed pattern is an easily memorized distillation of a labyrinth pattern, showing all of the turns at the main axis. For uniaxial labyrinths (Simple labyrinths: 1 axis, 1 sector), this represents the entire pattern. The use of seed patterns enabled the wide dissemination of the earliest Classical labyrinths, and they are still effective now thousands of years later. Slight variations of a single seed pattern allow for expression in a wide variety of styles.

Idealized Seed

For Simple labyrinths, this represents the entire pattern.

Cross Seed

General style choice:

squared turns

Hybrid Seed

General style choice:

squared and rounded turns

Diamond Seed

General style choice:

rounded turns

For Divided and Complex labyrinths, the main axis is just the starting point. These multiaxial labyrinths have mid-circuit turns and sector crossings at secondary axes, so thread diagrams are needed to show the complete pattern.

Classical 7 MCM Type

Main axis is sufficient for a complete Simple type.

Greys Court (aka Chartres Essence) Type

Secondary axes as well as main axis are needed for a complete Complex type.

Note: this type uses the same main axis as the Classical 7 MCM type.

Mathematical Efficiency of the Seed

Beyond its role in drawing or building a labyrinth, the seed pattern serves as a powerful mathematical filter. Instead of needing to test thousands of raw circuit permutations (see Quantum Potential State on the Conceptual Model page), seed patterns and the half seeds from which they are constructed allow us to reduce the options to a more manageable number of possibly viable types.

For smaller numbers of circuits, this may not seem significant. For example, there are only six permutations of three circuits (123, 132, 213, 231, 312, 321), so it is easy to find the two that are viable as Simple Alternating Transit (SAT) labyrinths (see below).

However, for 7-circuit SAT labyrinths, as a contrasting example, there are 5,040 permutations of circuits that have to be narrowed down to the 42 viable types. By identifying that there are only 14 possible 7-circuit half seeds, we only need to work with 196 combinations of those half seeds to find the 42 viable types (see below).

3-Circuit Permutations

0|123|4

viable as SAT

1 3 2

2 1 3

2 3 1

3 1 2

0|321|4

viable as SAT

1 of 2

fully serpentine

2 of 2

fully nested

Complexity Comparison with Increasingly Significant Efficiency

3 circuits:

6 circuit permutations ➞ 2 viable SAT types
2 front/back half seeds ➞ 4 half seed combinations ➞ 2 viable SAT types

4 circuits:

24 circuit permutations ➞ 3 viable SAT types
3 front and 2 back half seeds ➞ 6 half seed combinations ➞ 3 viable SAT types

5 circuits:

120 circuit permutations ➞ 8 viable SAT types
5 front/back half seeds ➞ 25 half seed combinations ➞ 8 viable SAT types

6 circuits:

720 circuit permutations ➞ 14 viable SAT types
9 front and 5 back half seeds ➞ 45 half seed combinations ➞ 14 viable SAT types

7 circuits:

5,040 circuit permutations ➞ 42 viable SAT types
14 front/back half seeds ➞ 196 half seed combinations ➞ 42 viable SAT types

7-Circuit SAT Half Seeds

In the image below, the 14 half seeds are each reflected on both sides of the main axis. Each of these half seeds can be paired with its reflection for a viable type. The remaining full seeds are formed by pairing two different half seeds from these 14 with a subset of these combinations being viable.

Half seeds can also be indicated using an alpha abbreviation for the pattern of serpentine turns, s, and nested turns, n, beginning at the outside (the bottom of these seed diagrams) and moving toward the center (the top). They are ordered below from least nested (fully serpentine) to most nested (fully nested). Parentheses in an sn pattern indicate turns within a nest.

The complete list and diagrams of the 42 7-circuit seed patterns (and others) will be available in my dissertation. Meanwhile, see the SAT Groups Summary document, the 1.7 SAT Groups page, and the table in the PDF below:

7c SAT Seed Permutations YZC.pdf

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