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.
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 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.
In Their Words
“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 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.”
“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.”
“It doesn't matter that much if you don't have a clear idea for a project, what you do in the end doesn't really matter, it seems like it would be fun doing any project.”
“It is a truly interdisciplinary and intercultural experience that I will never forget…
The NKS Summer School enabled me to learn many aspects of NKS and Mathematica and to be able to produce meaningful results in a very short time.”
“With the little I have seen, the world of learning should be getting ready for NKS take-over!”
“The NKS Summer School is an intellectual tour de force, with highly competent instructors and fellow students.”
“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.”
“If you want to see life, the universe, and everything else from a computing point of view, NKS Summer School is the right place to start!”
“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.”
“It's a great environment for students of everywhere with a lot of conversations about nature, computations, complexity, and new ideas arising in these current times.”
“All in all, quite an achievement.”
Advice for Future Attendees…
“Keep an open mind. Try to identify the most important directions to explore, and if stuck, break tasks down and run through all the subtasks starting with the easiest one.”
“Get ready for some serious intellectual stimulation!”
Read the book.
“Read the A New Kind of Science book. Prepare to meet people from many diverse backgrounds (This truly is one of the Summer School’s greatest strengths–everyone is from everywhere, and there are a variety of ages and education levels to be seen). Come up with a preliminary project idea. Practice the Wolfram Language with the provided problem sets.”
“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.”
“The only way to understand a complex system is to re-create it on your computer. NKS methods are the best.”
“Internalize the key points of NKS!”