Geometry of Boundary Exchanges
Bibliographic Data
| ID | 4491689 |
|---|---|
| Authors | Sandra Lach Arlinghau (0000-0001-5500-8825), Sandra L Arlinghaus, John D Nystuen |
| Year | 1990 |
| Volume | 80 |
| Issue | 1 |
| Pages | 21 |
| Publication date | 1990-01-01 |
| Open Access | Yes |
| Type | ARTICLE |
| Venue | Geographical Review (JOURNAL) |
| Journal identifiers | ISSN: 0016-7428 • E-ISSN: 1931-0846 |
| Publisher | JSTOR (PUBLISHER) |
| DOI | 10.2307/215895 |
| OpenAlex | W2033832163 |
| Language | EN |
| Citations received | 2 |
| References cited | 3 |
The geometric concept of self-similarity, from fractal geometry, may be used to compress portions of long, linear boundaries separating contrasting landuse types, like lake and shore or forest and meadow, into small, compact regions. This process is applied to maps of an actual location on the northern shore of Lake St. Clair and to a hypothetical map of a national forest. Using fractal geometry to determine boundaries can offer visitors to such regions the opportunity to enjoy exchange across them and can simultaneously minimize the potential for overall damage to broad expanses of shore or forest. V ISITORS to forests and to shorelines share a desire to experience the variety that the landscape has to offer, to do so in relative privacy, and to have direct access to the sites they come to visit. Of concern are finding a way to offer a full measure of public access and minimizing the potential for environmental damage. The fractal concept of self-similarity is such an approach to this issue of maximum exposure in minimum space. An analogous problem arises in telecommunications with the introduction of facsimile transmissions and other data-intensive media. The problem is to increase data transmission without exceeding capacity. Fractal methods are employed to achieve data compression, so that additional information may be transmitted within a fixed capacity (Barnsley 1988). We seek ways to increase exchange with the environment without exceeding its capacity for exposure to people. In this article we apply the fractal compression of boundaries used in electronic systems to the terrestrial environment. Previous research has shown such geometric boundary compression to be an effective means of reducing the entire geometry of central-place theory to single fractal transformations; in such cases, the compression comes about by finding a fractallike form to fit a landscape form (Arlinghaus 1985; Arlinghaus and Arlinghaus 1989). We begin our study with a brief explanation of self-similarity. We then illustrate how self-similarity might be applied in seashore and forest settings to con- struct interdigitated patterns of land and water or of forest and meadow, by compressing the boundaries separating them within a small parcel of land. This approach, we believe, can help resolve the dilemma of maximizing contact between humans and natural landscapes in a minimum of terrestrial space and with a minimum of environmental hazard. SELF-SIMILARITY
Boundary (topology · Geography · Geometry · Mathematical analysis · Geology · Mathematical Dynamics and Fractals · Mathematics · Stochastic processes and statistical mechanics · Theoretical and Computational Physics
| Citations per year | 0.06 |
|---|---|
| Citation span | 1993 - 2010 (18) |
| Highly cited | No |