Category Archives: Update

Julia Set Animation Part 1

Dear Readers

The Julia set has been one of my favorite fractals since when I first learned about fractals. The fractal is full of beautiful intricate curves and jagged edges. As such I am happy to share this animation of the Julia Set:

This animation consists of 1440 different Julia Sets on the equation z_{n+1} = z_n ^2 + c where c = .77 \cos (x) + .53 i \sin(x). Each image is 3600×3600 pixels with a max iteration of 100. Also feel free to check out some of the selected images.

659a

The resolution of our selected images are 7200×7200 and with a maximum iteration of 175.

For more selected images of this animation go here.

For more Fractals and Fun, visit the Fun Corner.

With best Wishes

WuFeng

A Crash Course in Deterministic Finite State Machines

Dear Readers,

Hi! This is WuFeng from WuFeng Engineering. Planning and modeling have always been solid ways to help reduce cost and mistakes. A model for computer software or hardware is the finite state machine.

Finite state machines are at the heart of computer science. In the systems side, it is used to model hardware and software before implementation, reducing unneeded work and errors. In theory, finite state machines have been augmented into Turing Machines and used to studying the very limits of computation with many open problems such as P vs NP.

This tutorial, “A Crash Course in Deterministic Finite State Machines” provides a brief look and tutorial to Deterministic Finite Automata. A basic understanding of Set Notation.

More on Finite State Machines such as Nodeterminism, Pushdown Automata and Turing Machines will be provided on a later date.

With Best Wishes

WuFeng

A Crash Course In Groups

Dear Readers

Hi! This is WuFeng from WuFeng Engineering, and I am here to present out fourth crash course tutorial “A Crash Course in Groups” which  serves as a continuation for “A Crash Course in Set Notation” and “A Crash Course in Modular Arithmetic“.

Modern abstract algebra is one of the largest fields in mathematics with countless applications to Physics, Chemistry, Material Science and Computer Science. One topic in Modern Algebra is the group. A group is a simple structure that can be used to represented many physical phenomena and aid in public key cryptosystems.

Our Tutorial, “A Crash Course in Groups” provides a brief introduction to the definition of a group and some examples. It is meant for those who are curious as well as those in need of a refresher.

As Always

With best wishes

WuFeng

A Crash Course on Set Notation

Dear Readers,

Hi! This is WuFeng from WuFeng Engineering and I am here to present our latest tutorial entitled “A crash course in set notation“.

Set notation is the language of modern mathematics and computer science. It allows for much needed formality and brevity by allowing one to define collections of objects and operations on them.

Set theory is the foundation for modern mathematics in fields such as Abstract Algebra and Topology. Set theory is needed in theoretical computer science as it creates ways to model computer programs before they are written. Because of its importance, A crash course in set notation, is meant as a quick and easy introduction for those who are interested in mathematics or computer science and for those who need a quick refresher.

More information on set theory, such as the axioms of set theory will be provided on a later date.

With best wishes

WuFeng

Proofs Made Easy

Dear Readers,

Mathematics is at the core of many of today’s innovations. It is the foundation of Physics and Engineering. It is used in finance and economics. It is used film and animation. However mathematics is more than basic computations. Mathematics is a study of reasoning and logic, as such the language of mathematics is proof.

A mathematical proof is a series of logical statements that shows the truth of a statement. Proofs are built from axioms and proven statements called theorems. Once a statement has been accurately proven to be true, it can never be proven false.

Proofs are not only restricted to Mathematicians, proofs are used by Physicists and Engineers in any situation where physical tests are too costly or impossible. Thus I am proud to present our tutorial “Proofs Made Easy“.

With Best Wishes

WuFeng