Conceptual Material: More of the MiniMax
Principle from the abstract to the "real."
of many forms seeks to minimize one property (or set of properties) while
maximizing another (hence, MiniMax). One sees this principle in both
conceptual and practical approaches.
Maximize contact between humans and natual landscapes
in a minimum of terrestrial space with minimal environmental hazard.
Viewed in the context of condos along the Great Lakes's perimeter, one
might ask how can individuals be offered the opportunity to secure desirable
shore sites without doing extensive overall damage to vast stretches of
shore line? Fractal geometry offers one solution by compressing shoreline
through a sequence of cuts involving scale change.
Mechanics of this fractal construction (more
detail, in a different context, later): replace each edge by a shape
involving a 95 degree cut (canal).
Characteristics of the construction as applied to condos.
Each condo pod has access to road on one side and shoreline on the other.
Both road and water networks have successively narrower routes based on
likely traffic--a hierarchy of widths
The two network trees are separate from each other. Appropriately
selected V-shaped cuts transform a shoreline length of x into one of length
32x, a 32-fold compression without adding any new area. The chosen
self-similarity transformation for generating slips and canals simultaneously
produces appropriately scaled roadways from trunk lines to driveways and
466 condominium pods, as well.
There are no bridges required--left-hand figure below
Any one may have a tall-masted boat
Infrastructure (pipes and so forth) is not exposed
One may choose relative position on either tree and find a pod to suit
those choices--right-hand figure below. Access to each pod is characterized
according to number of turns; the orientation of pod to slip is clockwise
across the entire figure (which accounts for lack of bilateral symmetry
in shading within the broader bilaterally symmetric geometric pattern).
Fewer water than land turns are required to reach 196 black pods--well-suited,
perhaps, to the avid sailor who will spend a continuous stretch of time
at the shore.
Equal number of water and land turns are required to reach 146 gray pods--well
suited to the sailor who often comes in and out with a boat trailer.
Fewer land than water turns are required to reach 124 white pods--well-suited
to the people who spend far more time in the car than on the water (perhaps
the elderly or infirm).
Worked with a developer to create such an arrangement on a difficult
parcel; dredging costs proved prohibitive. Sheltered aspect also
desirable for this site along Lake St. Clair with a shoreline subjected
to continuing wave action.
Based on material from:
Arlinghaus and J. Nystuen, "Geometry of Boundary Exchanges," Geographical
Review, Vol. 80, No. 1, 1990, The American Geographical Society, pp.
Hagerstrand's Simulation of Diffusion--see
material. The GIS may also be used to illustrate similar ideas:
spatial infill and extent.
Put down a dot for each adopter. Thus, one
shape file has 22 dots.
Create a new field in the attribute table and insert
associated random numbers.
Partition these dots into the six different categories
of the mean information field.
Use "Analysis" | "Neighborhood Statistic" to build
neighborhoods based on position of cell in relation to center of MIF.
Thiessen Polygons--another point and polygon