The analysis of spatial autocorrelation among point-data quadrats is a well-developed technique that has made limited but intriguing use of the multiscale aspects of pattern. In this paper are presented theoretical and algorithmic approaches to the analysis of aggregations of quadrats at or above a given density, in which these sets are treated as multifractal regions whose fractal dimension, D, may vary with phenomenon intensity, scale, and location. The technique is illustrated with Matui's quadrat house-count data, which yield measurements consistent with a nonautocorrelated simulated Poisson process but not with an orthogonal unit-step random walk. The paper concludes with a discussion of the implications of such analysis for multiscale geographic analysis systems.
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References
1.
AlonsoW, 1980, “Five bell shapes in development”Papers of the Regional Science Association455–16
BattyMFotheringhamASLongleyP, 1989, “Urban growth and form: Scaling, fractal geometry, and diffusion-linked aggregation”Environment and Planning A211447–1472
4.
BerkowitzSD, 1982An Introduction to Structural Analysis: The Network Approach to Social Research (Butterworth, Toronto)
5.
BesagJ, 1987, “On the statistical analysis of dirty pictures”Journal of the Royal Statistical Society, Section B48259–302
6.
BhaskarSKRosenfeldAWuAY, 1988, “Parallel processing of regions represented by linear quadtrees”Computer Vision, Graphics, and Image Processing42371–380
7.
BurroughPA, 1986Principles of Geographical Information Systems for Land Resources Assessment (Oxford University Press, Oxford)
8.
ClarkNN, 1986, “Three techniques for implementing digital fractal analysis of particle shape”Powder Technology4645–53
9.
ClarkWAVHoskingPL, 1986Statistical Methods for Geographers (John Wiley, New York)
10.
ClarkeKC, 1985, “A comparative analysis of polygon to raster interpolation method”Photogrammetric Engineering and Remote Sensing51575–582
CouclelisH, 1988, “Of mice and men: What rodent populations can teach us about complex spatial dynamics”Environment and Planning A2090–109
13.
CressieN, 1986, “Kriging nonstational data”Journal of the American Statistical Association81625–634
14.
De ColaL, 1989a, “Pareto and fractal description of regions from a binomial lattice”Geographical Analysis2174–81
15.
De ColaL, 1989b, “Fractal analysis of a classified Landsat scene”Photogrammetric Engineering and Remote Sensing55601–610
16.
De ColaL, 1989c, “Multiscale data models for spatial analysis, with applications to multifractal phenomena”, in Autocarto-9 (American Society for Photogrammetry and Remote Sensing and the American Congress on Surveying and Mapping, Church Falls, VA) pp 313–323
SoulieFogelman FRobertYTchuenteM, 1987Automata Networks in Computer Science (Princeton University Press, Princeton, NJ)
19.
GabrielPLovejoySSchertzerDAustinGL, 1988, “Multifractal analysis of resolution dependence in satellite imagery”Geophysical Research Letters151373–1376
20.
GetisAFranklinJ, 1987, “Second-order neighborhood analysis of mapped point patterns”Ecology68473–477
21.
GoodchildMF, 1980, “Fractals and the accuracy of geographical measures”Mathematical Geology12(2) 85–98
22.
GoodchildMFMarkDM, 1987, “The fractal nature of geographic phenomena”Annals of the Association of American Geographers77265–278
23.
GouldP, 1985The Geographer at Work (Routledge and Kegan Paul, Andover, Hants)
24.
GouldP, 1988, “What does chaos mean for theory in the human sciences?”, in Ground for Common Search Eds GolledgeRGCouclelisHGouldP (Santa Barbara Geographical Press, Goleta, CA) pp 11–30
25.
GriffithDA, 1987, “Toward a theory of spatial statistics: Another step forward”Geographical Analysis1969–82
26.
GutA, 1988Stopped Random Walks: Limit Theorems and Applications (Springer, New York)
27.
HägerstrandT, 1967Innovation Diffusion as a Spatial Process (University of Chicago Press, Chicago, IL)
28.
HaggettPCliffADFreyA, 1977Locational Analysis in Human Geography (Edward Arnold, London)
29.
LovejoySMandelbrotBB, 1985, “Fractal properties of rain, and a fractal model”Tellus37A209–232
30.
LovejoySSchertzerD, 1988, “Extreme variability, scaling and fractals in remote sensing: Analysis and simulation”, in Digital Image Processing Ed. MullerJP (Taylor and Francis, Philadelphia, PA)
31.
MandelbrotBM, 1983The Fractal Geometry of Nature (W H Freeman, New York)
32.
MarkDMAronsonPB, 1984, “Scale dependent fractal dimensions of topographic surfaces: An empirical investigation with applications to geomorphology and computer mapping”Mathematical Geology16671–683
33.
MasonDCCorrDGCrossAHoggDCLawrenceDHPetrouMTailorAM, 1988, “The use of digital map data in the segmentation and classification of remotely sensed images”International Journal of Geographic Information Systems2(3) 195–215
34.
MatuiI, 1932, “Statistical study of the distribution of scattered villages in two regions of the Tonami Plain, Toyama Prefecture”Japanese Journal of Geology and Geography9251–266
MullerJP (Ed.), 1988Digital Image Processing (Taylor and Francis, Philadelphia, PA)
37.
NicolisGPrigogineI, 1989Exploring Complexity (W H Freeman, New York)
38.
OrbachR, 1986, “Dynamics of fractal networks”Science231814–819
39.
ParrJBO'NeillGJ, 1989, “Aspects of the lognormal function in the analysis of regional population distribution”Environment and Planning A21961–973
40.
PetersonI, 1988The Mathematical Tourist (W H Freeman, New York)
41.
PeuquetDJ, 1988, “Representations of geographic space: Toward a conceptual synthesis”Annals of Association of American Geographers78375–394
42.
RaynerJNGolledgeRG, 1972, “Spectral analysis of settlement patterns in diverse physical and economic environments”Environment and Planning4347–371
43.
RobinsonAHSaleRDMorrisonJLMuehrckePC, 1984Principles of Cartography5th edition (John Wiley, New York)
44.
RogersA, 1974Statistical Analysis of Spatial Dispersion: The Quadrat Method (Pion, London)
45.
RudnickJGaspariG, 1987, “The shapes of random walks”Science237384–389
46.
SametHWebberRE, 1988, “Hierarchical data structures and algorithms for computer graphics part I: Fundamentals”IEEE Computer Graphics and Applications8(3) 48–68
47.
StanleyHEOstrowskyN, 1986On Growth and Form: Fractal and Non-fractal patterns in Physics (Martinus Nijhoff, Boston, MA)
48.
ToffoliT, 1988, “Pattern recognition and tracking by texture-locked loops”, technical memorandum, MIT Laboratory for Computer Science, Cambridge, MA 02139
49.
WolframS, 1984, “Cellular automata as models of complexity”Nature311419–424
50.
WoodcockCEStrahlerAH, 1987, “The factor of scale in remote sensing”Remote Sensing of Environment21311–332
