Today I was thinking about the Permaculture concept of zonation. In the most simplistic terms, zonation would advise that you place an element in the landscape according to how frequently you need to visit it. Elements that you need to visit frequently, such as your main garden, should be within zone 1 of your home. Other elements, like apple trees, in zone 3 and wild forest in zone 5. That is the general idea.

This concept of zonation arguably implies the use of single minimum heuristic that involves computing some distance metric between a landscape element, and your zone 0 reference point, and deciding if it satisfies some minimum distance metric for that landscape element. I call this Single Dimension Zonation and it is a powerful Permaculture idea. But it can be extended as follows.

Let H be your Home and G be a Garden element that you want to place in your landscape. Given this, we can compute the distance D between H and G where G is located at some specified landscape coordinate.

Let W be a second important constraint, Water, whose location we will denote with the letter W.

Where I want to place the garden G is not simply determined by how close it is to my home, e.g., min(G-H). An equally important consideration is how close it is to the water source I might want to use to irrigate it, e.g., min(G-W). The use of two constraints to compute a minimum might be called the Dual Zonation Heuristic for locating landscape elements.

So here is how it works.

If I place my garden G at location 1, the dual minimum is computed by first estimating the distance between my home H and garden location 1 (G₁ - H), then estimating the distance between my water source W and garden location 1 (G₁ - W). My estimate today was 20 feet from H to G and 30 feet from W to G for the garden at its' existing location. I then weight the importance of each dimension by multiplying each distance by a number beween 0 and 1. Using the value.5 for both dimensions expresses the idea of equal importance. I then add up each factor to get the average distance A.

A = (.5 * 20) + (.5 * 30)
A = 10 + 15
A = 25

So the average distance for location 1 is 25. I can pick other locations and see what their average distance is (say 26, 27, 28, etc...). Ultimately, I want to pick a garden location that is the minimum average score given my equal preference for the home nearness and water nearness constraints.

I'm in the situation, however, where I already have a garden in location 1 so I need to think in reverse to analyze the zonation that is being used. What are the weights I am assigning to the importance of the water source distance versus the house distance? I'm actually very satisfied with the location of the garden so computing these weights formalizes the degree of importance I am assigning to each constraint in this dual zonation analysis.

The use of dual zonation analysis allows me to finally understand why this old farm that we took over 6 years ago is laid out the way it is. Proximity to the house is only one factor, proximity to the main water source (a dug or spring source located in the garden shed that is no longer being used) was probably a more important consideration in determining the layout of the main barn, house, outbuildings and gardens. So we might regard dual zonation as a "landscape reading" technique that might help you to better understand why the built or natural landscape is organized as it is. You can visually triangulate distances between two landmarks (e.g., house and water source) and your garden and visually sense the weight structure that location selection expresses.

An application of triple zonation would be for the location of a "GetAway Cabin" on my farm property that would involve the selection of three reference points (zero points) from which distances would be computed:

F - Proximity to a forested/wild area
W - Proximity to a water source
R - Proximity to a road

Given these three types of constraints/zones, I can search for a location that is a minimum distance accross these three constraints. That location is where I would locate the "GetAway Cabin". Here is where I think it might be: At the end of a road through my field (road source), near a marsh that turns into a creek (water source), nestled besides a green belt of woods (wilderness source). Here is the future site of a "GetAway Cabin".

One more factor that was extremely important in my selection but which is still not included as a constraint is "privacy". I wanted a location where people can't see me and I can run naked in the woods if I want to :-) How should "privacy" be factored into a zonation analysis? Do we convert it into a distance or do we invoke the Permaculture concept of "sectors" and say that the selection must also satisfy a sector analysis for privacy as well? I think the latter is how I would proceed and not try to incorporate privacy as a spatial dimension. On the other hand, physical privacy does have spatial properties so don't hold me to that.