Data Acquisition

For visualization, a voxelized representation of phase-space and the objects of interest have to be obtained. As this requires extensive iteration of the difference equations which define the map, simulation and voxelization are performed off-line. The simulation process creates a set of volumes ($256^3$ voxels each), which contain basin-labeling information (which basin does the voxel belong to?), visit-count information for attractor voxels (how frequently is the voxel visited during iteration?), distance volumes which store the distance to the closest attractor voxel, and further volumes storing information required for the construction of critical surfaces. A post-processing step extracts objects' voxels (attractor voxels, basin-boundary voxels and critical-surface voxels) for storage and later viewing. The time to perform a single simulation is 3-10 minutes on a PII/500 PC with sufficient memory. Frequently, the creation of whole parameter sequences of data sets is required, varying the value of some dynamical system parameters for each step. To efficiently carry out simulation in such cases, a cluster of distributed computational servers is used (figure 7.3). As the simulation of different parameter steps can be performed independently of each other, the computation of each step can be assigned to any free computational server. Scheduling of the jobs is performed by a master server, which collects the results of the simulation and returns them to the requesting client. Even though extracted voxel data is stored instead of entire volumes, simulation sequences with tens or hundreds of parameter steps can easily produce 100-300 MB of data.

Figure 7.3: Computation of a parameter sequence simulation using a computational cluster

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