Fractals and disordered systems
Fractals and disordered systems
An Algorithm for Finding Best Matches in Logarithmic Expected Time
ACM Transactions on Mathematical Software (TOMS)
Chaos and Fractals
Foundations of Multidimensional and Metric Data Structures (The Morgan Kaufmann Series in Computer Graphics and Geometric Modeling)
Validity of the single processor approach to achieving large scale computing capabilities
AFIPS '67 (Spring) Proceedings of the April 18-20, 1967, spring joint computer conference
The study of terrain simulation based on fractal
WSEAS Transactions on Computers
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A simple an effective algorithm for performing distance queries between a large number of points stored in quadtrees and octrees. The algorithm is developed and tested for the construction of diffusion-limited aggregates. To achieve an enhancement on the searching time we accept approximate distance values with low precision at the first levels of the hierarchical structure, and accurate ones at the last level. The structure of the trees is the only feature used for the determination of approximate distances at any stage. These techniques allowed us to build DLA clusters with up to 109 particles for the two-dimensional case and up to 108 particles for the three-dimensional case. We also worked with the PDLA model obtaining fractal clusters with up to 1010 and 109 particles for two and three dimension clusters respectively. We worked on a supercomputer to run the PDLA simulations, as well as a high performance server for DLA simulations. We employed POSIX threads to provide parallelization and mutexes as control mechanisms to achieve synchronization between groups of 4 processors, hence simulating PDLA clusters with early convergence to the DLA model.