Paul D. Bourke

Spherical mirror: a new approach to hemispherical dome projection

Planetariums and smaller personal domes can provide an immersive environment for science education, virtual reality, and entertainment [Shaw 1998]. Digital projection into domes, called full dome projection in the industry, can be a technically challenging and expensive exercise, particularly so for installations with modest budgets. An alternative full dome digital projection system is presented based upon a single projector and a spherical mirror to scatter the light onto the dome surface. The approach offers many advantages over the fisheye lens alternatives, results in a similar quality result, but at a fraction of the cost.

Intrinsic connections in tree shrew V1 imply a global to local mapping

The local-global map hypothesis states that locally organized response properties--such as orientation preference--result from visuotopically organized local maps of non-retinotopic response properties. In the tree shrew, the lateral extent of horizontal patchy connections is as much as 80-100% of V1 and is consistent with the length summation property. We argue that neural signals can be transmitted across the entire extent of V1 and this allows the formation of maps at the local scale that are visuotopically organized. We describe mechanisms relevant to the formation of local maps and report modeling results showing the same patterns of horizontal connectivity, and relationships to orientation preference, seen in vivo. The structure of the connectivity that emerges in the simulations reveals a hub and spoke organization. Singularities form the centers of local maps, and linear zones and saddle-points arise as smooth border transitions between maps. These findings are used to present the case for the local-global map hypothesis for tree shrew V1.

Contribution of lateral interactions in V1 to organization of response properties

We propose a model of self-organization of synaptic connections in V1, emphasizing lateral interactions. Subject to Hebbian learning with decay, evolution of synaptic strengths proceeds to a stable state in which all synapses are either saturated, or have minimum pre/post-synaptic coincidence. The most stable configuration gives rise to anatomically realistic local maps, each of macro-columnar size, and each organized as Mobius projections of retinotopic space. A tiling of V1, constructed of approximately mirror-image reflections of each local map by its neighbors is formed, accounting for orientation-preference singularities, linear zones, and saddle points-with each map linked by connections between sites of common orientation preference. Ocular dominance columns are partly explained as a special case of the same process. The occurrence of direction preference fractures always in odd numbers around singularities is a specific feature explained by the Mobius configuration of the local map. Effects of stimulus velocity, orientation relative to direction of motion, and extension, upon orientation preference, which are not accounted for by spatial filtering, are explained by interactions between the classic receptive field and global V1.

Image processing of finite size rat retinal ganglion cells using multifractal and local connected fractal analysis

Automated image processing has great potential to aid in the classification of biological images Many natural structures such as neurons exhibit fractal properties, and measures derived from fractal analysis are useful in differentiating neuron types When fractal properties are not constant in all parts of the neuron, multifractal analysis may provide superior results We applied three methods to elucidate the variation within 16 rat retinal ganglion cells: local connected fractal dimension (LCFD), mass-radius (MR) and maximum likelihood multifractal (MLM) analyses The LCFD method suggested that some of the neurons studied are multifractal The MR method was inconclusive due to the finite size of the cells However, the MLM method was able to show the multifractal nature of all the samples, and to provide a superior multifractal spectrum We conclude that the latter method warrants further attention as it may improve results in other application areas.

Visualising chaos in a model of brain electrical activity

Abstract It is a major source of contention in brain dynamics as to whether the electrical rhythms of the brain show signs of chaos. Here we discuss evidence for the existence of chaos in a theory of brain electrical activity and provide unique depictions of the dynamics of this model.

Chaos and Graphics: An introduction to the Apollonian fractal

This paper provides an introduction to the Apollonian fractal, also known by some as the curvilinear Sierpinski gasket. This fractal is not particularly well known, perhaps because it is not as straightforward to construct as many other fractals such as the related Sierpinski gasket or the Menger sponge. The brief history and a general description of the fractal will be given, including the geometric construction in two dimensions and an iterated function system (IFS) formulation.

Visualizing astronomy data using VRML

Visualisation is a powerful tool for understanding the large data sets typical of astronomical surveys and can reveal unsuspected relationships and anomalous regions of parameter space which may be difficult to find programatically. Visualisation is a classic information technology for optimising scientific return. We are developing a number of generic on-line visualisation tools as a component of the Australian Virtual Observatory project. The tools will be deployed within the framework of the International Virtual Observatory Alliance (IVOA), and follow agreed-upon standards to make them accessible by other programs and people. We and our IVOA partners plan to utilise new information technologies (such as grid computing and web services) to advance the scientific return of existing and future instrumentation. Here we present a new tool - VOlume - which visualises point data. Visualisation of astronomical data normally requires the local installation of complex software, the downloading of potentially large datasets, and very often time-consuming and tedious data format conversions. VOlume enables the astronomer to visualise data using just a web browser and plug-in. This is achieved using IVOA standards which allow us to pass data between Web Services, Java Servlet Technology and Common Gateway Interface programs. Data from a catalogue server can be streamed in eXtensible Mark-up Language format to a servlet which produces Virtual Reality Modeling Language output. The user selects elements of the catalogue to map to geometry and then visualises the result in a browser plug-in such as Cortona or FreeWRL. Other than requiring an input VOTable format file, VOlume is very general. While its major use will likely be to display and explore astronomical source catalogues, it can easily render other important parameter fields such as the sky and redshift coverage of proposed surveys or the sampling of the visibility plane by a rotation-synthesis interferometer.