Apparent Fractality Emerging from Models of Random Distributions

The fractal properties of models of randomly placed $n$-dimensional spheres ($n$=1,2,3) are studied using standard techniques for calculating fractal dimensions in empirical data (the box counting and Minkowski-sausage techniques). Using analytical and numerical calculations it is shown that in the regime of low volume fraction occupied by the spheres, apparent fractal behavior is observed for a range of scales between physically relevant cut-offs. The width of this range, typically spanning between one and two orders of magnitude, is in very good agreement with the typical range observed in experimental measurements of fractals. The dimensions are not universal and depend on density. These observations are applicable to spatial, temporal and spectral random structures. Polydispersivity in sphere radii and impenetrability of the spheres (resulting in short range correlations) are also introduced and are found to have little effect on the scaling properties. We thus propose that apparent fractal behavior observed experimentally over a limited range may often have its origin in underlying randomness.Comment: 19 pages, 12 figures. More info available at http://www.fh.huji.ac.il/~dani

RANDOM AMPLIFIED POLYMORPHIC DNA ANALYSIS OF AUSTRALIAN RICE (ORYZA-SATIVA L) VARIETIES

The genetic relationships between rice varieties were analysed by using the polymerase chain reaction (PCR), with arbitrary oligonucleotide primers in the random amplified polymorphic DNA (RAPD) method. PCR with 22 arbitrary primers applied to 37 varieties produced 144 useful markers, of which 67% were polymorphic. Thus, with selected primers sufficient polymorphism could be detected to allow identification of individual varieties. Visual examination of electrophoresis gels and analysis of banding patterns confirmed that commercial Australian and USA lines and their relatives were very closely related, with similarity indices of 88-97%. Three varieties originating from more distant geographical centres were easily distinguished, producing variety-specific amplification profiles and expressing a lower similarity index of 80% to all other varieties tested. PCR offers a potentially simple, rapid and reliable method for rice genotype identification and recognition of lines that could contribute genetic diversity to new commercial varieties