Fractals and Chaos Simplified for the Life Sciences

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Page 262
dimension 46
fractal 64
phase space 130
scaling 28
self-similarity 12
sensitivity to initial conditions 162
statistical properties of fractals 74
strange 168
Delbruck 93
Destexhe 197, 199
deterministic
but not predictable 162-165
mechanisms 116-126
phase space 122, 126, 136, 148
vs. random 116-119, 122, 126, 136, 142, 148, 152, 188, 192
ion channels 200-205
problems with the analysis 206-217, 222
surrogate data sets 220-221
vectors in phase space 218, 219
Diamond 197
diffusion limited aggregation (DLA) 70, 80, 81
dimension (Part I, Chapter 4) 45-71
biological implications 70
blood vessels in the lungs 66, 67
box counting 56, 57
capacity 47, 50-52, 56
covering 47, 60, 61
definition 46
deterministic mechanism 122, 126, 136, 142, 148
embedding 46, 62, 138, 142
examples 68
fractal
biological fractals 66-69
biological chaos 140, 141, 146, 194-199
definition 64, 65
phase space 122, 126, 134,-137, 142, 148, 150, 168
types 46-59
Hausdorff-Besicovitch 47, 52, 53
iterative 47, 60, 61
logistic equation 122, 123, 127, 134-137
Lorenz equations 134, 135, 158
not equal to the dimension 150, 151
number of independent variables 134
phase space 122, 126, 136, 138, 142, 148
problems with the phase space analysis 206-217, 222
random mechanism 122, 126, 136, 142, 148, 150, 168, 194-199, 210-217, 222
scaling 58
self-similarity 47-49, 54
topological 46, 47, 60, 61, 64
Ding 211
distributions
fractal 70, 84, 102, 104
Gaussian 70, 84, 86, 102, 104
Poisson 86
probability density function (pdf) 12, 20, 21
pulse number 84-87
stable 70, 102, 104
Ditto 231
DNA 100
dynamical systems 124, 240
E
ear 84-87, 140, 141
Edgar 111
Eldred 15

 
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