Matrices and the Strategies of Compacting and Complexing Components

Permaculture Designers Manual




Section 4.3 –

Matrices and the Strategies of Compacting and Complexing Components

A set of intersecting sine waves developed over a regular square or hexagonal matrix will set up a surface composed of our core model shapes.

It doesn’t matter if we see the sine waves as static or flowing, the core model will still maintain its shape, and flow in the system does not necessarily deform the pattern.

Such a pattern matrix (Figure 4.2) shows that our models tessellate (from the Latin tessarae, meaning tiles) to create whole surfaces. If landscapes are, in fact, a set of such models, they must be able to tessellate.

Convection cells on deserts arise from a roughly hexagonal matrix of air cells 1-5 km across, and matrices also underlie the spacing of trees in forests.

Glacial landscapes show whole series of such patterns, as do regular river headwaters. We could equally well have created a matrix by adding in samples of our core pattern as we add tiles to a floor.

Thus we see the Euclidean concept of points and lines underlies our curvilinear forms.

Even irregular models (Figure 4.3) tessellate. Such tessellae are centered on nets or regular grids.

Further; a set of our models, invading into or generating from, a portion of the landscape produce EXPANSION and CONTRACTION forms (Figure 4.4) typical of the edges of inland dunes and salt pans. This crenellated (wavy) edge produces edge harmonics of great relevance to design.

The study of matrices reveals that the T (time) lines are ogives of a tessellated model and develop from the “S” (stream) lines of the next model adjoining. We then come to understand something of the co-definitions in our core model, and its inter-dependent properties.  Sets of such models and their marginal crenellations provide a complex interface in natural systems, often rich in production potential.

The earth itself is “a great tennis ball” (N Scientist, 21 April, 77) formed of two core model forms. This earth pattern (Figure 4.5) of two nested core models can be re-assembled into a single continent and one sea if the present globe is shrunk to 80% of its present diameter.

My old geology professor, Warren (“Sam”) Carey may have been justified in his 1956 assertion that the earth was originally that much smaller.

When re-assembled in this way, the globe shows an origin (“O” of our model) over each pole; the north polar origin is that of the seas, the Antarctic origin that of the continents .

At that time in earth history, all life forms were native to a single continent and all fish swam in one sea.

The original pattern shattered, continents now drift, collide, and form their own life pattern by isolation, recombination, and the slow migration of natural processes.

The process also illustrates how irregularities may arise on an expansion of a previously regular matrix of forms; tension caused by expanding phenomena shatters the smooth flow of primary global events.

At the end of a certain energy sequence, old patterns shatter or erode to make way for new patterns and succeeding forms of energy, as a decaying tree gives life to fungi and to other trees.

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