A unique opportunity to do original research at the frontiers of science, the Wolfram Science Summer School helps about 40 students from a diverse range of scientific backgrounds learn about Stephen Wolfram's A New Kind of Science (NKS) and apply it to their fields of interest. Most of these students are advanced undergraduates and early graduate students, but those in different circumstances are considered. We are looking for students who want to move their careers in the NKS direction. Read more »
I identified four kinds of symmetric fractal trees in 3D that are determined by the type of expressions found in their boundary equations; these are trees with number of branches b=4n-1, b=4n, b=4n+1 and b=4n+2 where n takes the integer values from 1 to ¶. Several animations were produced when one walks around the critical boundaries of the parameter space, showing interesting dynamics and topological critical changes for certain angles.
My project consisted of a set of functions that can extract a plot dataset when provided the vector representation of the plot. I have been able to successfully identify axes, ticks, labels, and data points for my self-generated plots. In this situation the error is negligible and depends mainly on a geometric object with nonzero area used to identify the points in the set.
The aim of this project is to identify the manifolds corresponding to networks that are generated by simple substitution rules from Stephen Wolfram's physics project. At first glance, some of the networks resemble a cell complex of a known surface.The idea is to provide techniques to substantiate this impression and figure out the geometric structure that might underlie the purely combinatorially given network.
We propose to explore a number of analytical galaxy rotation curves to create a template library of cellular automata galaxies. A quantitative measure of galaxy morphology needs to be ascertained to compare observations (perhaps at multiple wavelengths) to the CA galaxies. Polar basis functions consisting of Chebyshev rational functions TLn(r) and Fourier series (Jimenez-Teja & Benitez 2011) can be applied to the. The basis coefficients for observations and models can be used as a figure of merit or metric for comparison, matching CA simulation galaxies to sets of cataloged images via the parameterized effective radius.
We consider 2-dimensional block cellular automata (BCA) with intention to meet simple physical requirements such as reversibility and space isotropy. Along with general study of the whole class of 2x2-neighborhood BCA, several rule subspaces that meet physical criteria are studied. It is also interesting to examine the possibility of the energy conservation expressed in terms of local rules. The energy function is set by the Ising model. Interpretation of domain, oscillating, particle and other patterns in terms of physical phenomena were studied. Some statements about impossibility of energy conservation laws expressed by 2D 2x2 BCA local rules were proved and verified experimentally with filtration methods.
We have devised a simple way to introduce temporary perturbations in trinet computations and have visualized their effects by the revisit indicator, which turns out to be especially useful for this purpose. This technique can indeed be used also for exploring behaviors starting from random initial conditions.
I enjoyed the experience and learned a lot from other students, instructors, and my mentor. The idea of looking through a defined space, searching for the interesting cases is fascinating and will change how I research, because you never know what you will find.
The best thing that happened to me in July 2013 was attending the Wolfram Science Summer School! Its memories will linger, and the knowledge gathered will forever be handy. I can't predict the future, but I am confident of this.
The Wolfram Science Summer School is an amazing multi-disciplinary and multicultural experience. It changes your mind, the way you usually work, gives you more points of view, and helps you for your career.
It's a learning experience for anyone interested in being a part of an exciting new frontier. I got the sense of being one of a large group of people working to build the groundwork for this new science.
The primary value of the NKS Summer School to me was in making it clear what NKS is all about. It is about applying a new mode of thinking to the solution of scientific problems. This has enabled me to look at my research on new ways and has given me new pathways toward solutions to problems.
Learn as much Mathematica as possible beforehand. Try to find a project topic before the school and prepare for it by reading related background material, with emphasis on the relevant parts of the NKS book. In order to help this, browse the booklet of Open NKS Problems.
Attend the Conference, which will set the scene for your new train of thought process and throughout the conference you will get to know a bunch of interesting individuals. Think about what your project will be on; formulate a question and think about how you will be able to solve that.