210
Applications of Fractal Geometry and Percolation Theory to Landscape Analysis and Assessments
Ludwig, D. D.; Jones, D.; Holling, C. S. 1978. Qualitative analysis of insect outbreak systems: the spruce
budworm and the forest. J. Anim. Ecol. 44:315-332.
MacKay, G.; Jan, N. 1984. Forest fires as critical phenomena. J. Phys. A 17:L757-L760.
Mandelbrot, B. B. 1977. Fractals: fonn, chance and dimension. New York: W. H. Freeman.
Mandelbrot, B. B. 1983. The fractal geometry of nature.
New York: W. H. Freeman.
Mandelbrot, B. B. 1989. Fractal geometry: what is it, and
what does it do? Proc. Roy. Soc. London A 423:3-16.
Mandelbrot, B. B. 1990. Negative fractal dimensions and
multifractals. Physica A 163:306-315.
Milne, B. T. 1988. Measuring the fractal geometry of
landscapes. Appl. Math. Comput. 27:67-79.
Milne, B. T. 1990. Lessons from applying fractal models to landscape patterns. In: Turner, M. G.; Gardner,
R. H., eds. Quantitative methods in landscape ecology. New York: Springer-Verlag: 199-235.
Milne, B. T. 1992. Spatial aggregation and neutral models in fractal landscapes. Amer. Naturalist 139:32-57.
Milne, B. T.; Johnson, A. R; Keitt, T. H.; Hatfield,
C. A.; David, J.; Hraber, P. 1996. Detection of critical densities associated with pinon-juniper woodland
ecotones. Ecology 77:805-821.
Mollison, D. 1977. Spatial contact models for ecological and epidemic spread. J. Roy. Statist. Soc. B 39:
283-326.
Mollison, D. 1986. Modelling biological invasions:
chance, explanation, prediction. Phil. Trans. Roy. Soc.
London B 314:675-693.
Montgomery, D. R.; Dietrich, W. E. 1992. Channel initiation and the problem of landscape scale. Science
255:826-830.
O'Neill, R V.; Milne, B. T.; Turner, M. G.; Gardner,
R. H. 1988. Resource utilization scales and landscape
pattern. Landscape Ecol. 2:63-69.
Palmer, M. W. 1988. Fractal geometry: a tool for describing spatial patterns of plant communities. Vegetatio 75:91-102.
Palmer, M. W. 1992. The coexistence of species in fractal landscapes. Amer. Naturalist 139:375-397.
Patil, G. P.; Taillie, C. 1989. Probing encountered data,
meta analysis and weighted distribution methods.
CSEES Technical Report No. 89-0101: 1-46.
Pielou, E. C. 1977. Mathematical ecology. New York:
John Wiley & Sons: 291-311.
Pietronero, L.; Tosatti, E., editors. 1986. Fractals in
physics. Amsterdam: North-Holland.
Pimm, S. T.; Gilpin, M. E. 1989. Theoretical issues in
conservation biology. In: Roughgarden, J.; May,
R M.; Levin, S. A., eds. Perspectives in ecological
theory. Princeton, NJ: Princeton University Press:
287-305.
Rex, K. D.; Malanson, G. P. 1990. The fractal shape of
riparian forest patches. Landscape Eco/. 4:249-258.
Risser, P. G. 1995. The status of the science examining
ecotones. BioScience 45:318-325.
Ruelle, D. 1989. Chaotic evolution and strange attractors. Cambridge, UK: Cambridge University Press.
Sahimi, H. 1994. Applications of percolation theory.
London: Taylor & Francis.
Shannon, C. 1948. A mathematical theory of communication. Bell Tech. J. 27:379-423, 623-656.
Stauffer, D. 1985. Introduction to percolation theory.
London: Taylor & Francis.
Stinchcombe, R B. 1990. Fractals, phase transitions and
criticality. In: Fleischmann, M.; Tildesley, D. J.; Ball,
R c., eds. Fractals in the natural sciences. Princeton,
NJ: Princeton University Press: 17-33.
Stockmayer, W. H. 1943. Theory of molecular size distribution and gel formation in branched chain polymers. J. Chem. Phys. 11:45-55.
Sugihara, G.; May, R M. 1990. Applications of fractals
in ecology. TREE 5:79-86.
Taylor, S. J. 1986. The measure theory of random fractals. Math. Proc. Camb. Phil. Soc. 100:383-406.
Turcotte, D. L. 1986. Fractals and fragmentation. J. Geophys. Res. 91:1921-1926.
Uzunov, D. I. 1993. Introduction to the theory of critical phenomena: mean field, fluctuations and renormalization. Singapore: World Scientific.
Voss, R F. 1988. Fractals in nature: from characterization to simulation. In: Peitgen, H.; Saupe, D., eds. The
science of fractal images. New York: SpringerVerlag: 21-70.
Wamer, W. S.; Fry, G. 1990. Evaluating small-format
photogrammetry for forest and wildlife surveys: Euclidean vs. fractal geometry. For. Ecol. Manage. 31:
101-108.
Wiens, J. A. 1992. Ecology 2000: an essay on future directions in ecology. Bull. ESA 73:165-170.
Wiens, J. A.; Milne, B. T. 1989. Scaling of "landscapes"
in landscape ecology, or, landscape ecology from a
beetle's perspective. Landscape Eco/. 3:87-96.
Williamson, M. H.; Lawton, J. H. 1991. Fractal geometry of ecological habitats. In: Bell, S. S.; McCoy,
E. D.; Mushinsky, H. R, eds. Habitat structure. London: Chapman and Hall: 69-86.
Wu, H.; Malafant, K. W. J.; Penridge, L. K.; Sharpe,
P. J. H.; Walker, J. 1987. Simulation of two-dimensional point patterns: application of a lattice framework approach. Ecol. Model. 38:299-308.
Young, I. M.; Crawford, J. W. 1991. The fractal structure of soil aggregates: its measurement and interpretation. J. Soil Sci. 42:187-192.
Zeide, B. 1991. Fractal geometry in forestry applications.
For. Ecol. Manage. 46:179-188.
Applications of Fractal Geometry and Percolation Theory to Landscape Analysis and Assessments
Ludwig, D. D.; Jones, D.; Holling, C. S. 1978. Qualitative analysis of insect outbreak systems: the spruce
budworm and the forest. J. Anim. Ecol. 44:315-332.
MacKay, G.; Jan, N. 1984. Forest fires as critical phenomena. J. Phys. A 17:L757-L760.
Mandelbrot, B. B. 1977. Fractals: fonn, chance and dimension. New York: W. H. Freeman.
Mandelbrot, B. B. 1983. The fractal geometry of nature.
New York: W. H. Freeman.
Mandelbrot, B. B. 1989. Fractal geometry: what is it, and
what does it do? Proc. Roy. Soc. London A 423:3-16.
Mandelbrot, B. B. 1990. Negative fractal dimensions and
multifractals. Physica A 163:306-315.
Milne, B. T. 1988. Measuring the fractal geometry of
landscapes. Appl. Math. Comput. 27:67-79.
Milne, B. T. 1990. Lessons from applying fractal models to landscape patterns. In: Turner, M. G.; Gardner,
R. H., eds. Quantitative methods in landscape ecology. New York: Springer-Verlag: 199-235.
Milne, B. T. 1992. Spatial aggregation and neutral models in fractal landscapes. Amer. Naturalist 139:32-57.
Milne, B. T.; Johnson, A. R; Keitt, T. H.; Hatfield,
C. A.; David, J.; Hraber, P. 1996. Detection of critical densities associated with pinon-juniper woodland
ecotones. Ecology 77:805-821.
Mollison, D. 1977. Spatial contact models for ecological and epidemic spread. J. Roy. Statist. Soc. B 39:
283-326.
Mollison, D. 1986. Modelling biological invasions:
chance, explanation, prediction. Phil. Trans. Roy. Soc.
London B 314:675-693.
Montgomery, D. R.; Dietrich, W. E. 1992. Channel initiation and the problem of landscape scale. Science
255:826-830.
O'Neill, R V.; Milne, B. T.; Turner, M. G.; Gardner,
R. H. 1988. Resource utilization scales and landscape
pattern. Landscape Ecol. 2:63-69.
Palmer, M. W. 1988. Fractal geometry: a tool for describing spatial patterns of plant communities. Vegetatio 75:91-102.
Palmer, M. W. 1992. The coexistence of species in fractal landscapes. Amer. Naturalist 139:375-397.
Patil, G. P.; Taillie, C. 1989. Probing encountered data,
meta analysis and weighted distribution methods.
CSEES Technical Report No. 89-0101: 1-46.
Pielou, E. C. 1977. Mathematical ecology. New York:
John Wiley & Sons: 291-311.
Pietronero, L.; Tosatti, E., editors. 1986. Fractals in
physics. Amsterdam: North-Holland.
Pimm, S. T.; Gilpin, M. E. 1989. Theoretical issues in
conservation biology. In: Roughgarden, J.; May,
R M.; Levin, S. A., eds. Perspectives in ecological
theory. Princeton, NJ: Princeton University Press:
287-305.
Rex, K. D.; Malanson, G. P. 1990. The fractal shape of
riparian forest patches. Landscape Eco/. 4:249-258.
Risser, P. G. 1995. The status of the science examining
ecotones. BioScience 45:318-325.
Ruelle, D. 1989. Chaotic evolution and strange attractors. Cambridge, UK: Cambridge University Press.
Sahimi, H. 1994. Applications of percolation theory.
London: Taylor & Francis.
Shannon, C. 1948. A mathematical theory of communication. Bell Tech. J. 27:379-423, 623-656.
Stauffer, D. 1985. Introduction to percolation theory.
London: Taylor & Francis.
Stinchcombe, R B. 1990. Fractals, phase transitions and
criticality. In: Fleischmann, M.; Tildesley, D. J.; Ball,
R c., eds. Fractals in the natural sciences. Princeton,
NJ: Princeton University Press: 17-33.
Stockmayer, W. H. 1943. Theory of molecular size distribution and gel formation in branched chain polymers. J. Chem. Phys. 11:45-55.
Sugihara, G.; May, R M. 1990. Applications of fractals
in ecology. TREE 5:79-86.
Taylor, S. J. 1986. The measure theory of random fractals. Math. Proc. Camb. Phil. Soc. 100:383-406.
Turcotte, D. L. 1986. Fractals and fragmentation. J. Geophys. Res. 91:1921-1926.
Uzunov, D. I. 1993. Introduction to the theory of critical phenomena: mean field, fluctuations and renormalization. Singapore: World Scientific.
Voss, R F. 1988. Fractals in nature: from characterization to simulation. In: Peitgen, H.; Saupe, D., eds. The
science of fractal images. New York: SpringerVerlag: 21-70.
Wamer, W. S.; Fry, G. 1990. Evaluating small-format
photogrammetry for forest and wildlife surveys: Euclidean vs. fractal geometry. For. Ecol. Manage. 31:
101-108.
Wiens, J. A. 1992. Ecology 2000: an essay on future directions in ecology. Bull. ESA 73:165-170.
Wiens, J. A.; Milne, B. T. 1989. Scaling of "landscapes"
in landscape ecology, or, landscape ecology from a
beetle's perspective. Landscape Eco/. 3:87-96.
Williamson, M. H.; Lawton, J. H. 1991. Fractal geometry of ecological habitats. In: Bell, S. S.; McCoy,
E. D.; Mushinsky, H. R, eds. Habitat structure. London: Chapman and Hall: 69-86.
Wu, H.; Malafant, K. W. J.; Penridge, L. K.; Sharpe,
P. J. H.; Walker, J. 1987. Simulation of two-dimensional point patterns: application of a lattice framework approach. Ecol. Model. 38:299-308.
Young, I. M.; Crawford, J. W. 1991. The fractal structure of soil aggregates: its measurement and interpretation. J. Soil Sci. 42:187-192.
Zeide, B. 1991. Fractal geometry in forestry applications.
For. Ecol. Manage. 46:179-188.