Unit 1 - Introduction to Nonlinear Dynamics

Nonlinear Dynamics: Mathematical and Computational Approaches is an (excellent) online course offered by Complexity Explorer. Unit 1 provided a general introduction to nonlinear dynamics and maps covering the following topics:

  1. Introduction to nonlinear dynamics
  2. Maps and difference equations
  3. Transients and attractors
  4. Parameters and bifurcations
  5. Field trip: Boulder Creek

Flexagons and the Math Behind Twisted Paper

Below I’ve collected my notes taken during the FutureLearn 3-week online course “Flexagons and the Math Behind Twisted Paper” presented by Dr. Yossi Elran of Davidson Institute of Science Education, Weizmann Institute of Science. This was a fascinating introduction to Flexagons and symbols to describe them, Möbius band, Catalan numbers and more. These are pretty rough notes at the moment, probably not very meaningful to those who haven’t taken this course.


Hello and welcome! I’m a web developer located in Baltimore, MD. My interests include computer graphics and animation, virtual/augmented/mixed reality, fluid dynamics, dynamical systems, maths, physics, and natural sciences. If it really takes 10,000 hours to achieve mastery in one of these topics, I’ll probably never achieve it, but hey - in the end it’s the journey that matters. :) And the journey is what this site is for. It’s a place to collect my notes about everything I’ve learned or made.

Night at the Museum

Introduction Night at the Museum is my final project in the second term of Udacity’s VR Developer Nanodegree program. This term focused on VR design and development process, VR platforms and the industries impacted by VR. This term introduced me to an incredibly wide range of applications I wasn’t aware of previously. My last thought-experiments (part1, part 2, and part 3) also helped me realize that there’s so much more than just ‘VR’ and that the future may really lie within the full spectrum of realities ranging from augmented reality, augmented virtuality, mixed reality to fully virtual reality.

The Puzzler VR Project

Introduction Welcome to my Puzzler project writeup! This project is part of Udacity’s VR Developer Nanodegree program. The second term of this program focuses on VR design and the development cycle from the initial statement of purpose, definition of a user persona, to the iterative process of creating a usable mobile app. This process involved multiple user tests to ensure that the experience is comfortable and clear to the player.

Astronomy: Exploring Time and Space - Week 4

The Tools of Astronomy Telescopes Gallileoscope 1 inch diameter over 400 years ago, modern telescopes now have diameters of 8 or 10 meters. Telescopes can also be used in invisible light wavelengths, e.g. ultraviolet, infrared, radio. James Webb Space Telescope will bring space astronomy to the level of large ground telescopes, 6.5 meter mirror. Ground based telescopes cost about a billion dollars. Hubble Space Telescope cost about $6-8 billion.

KaTeX, Khan Academy's Math Typesetting Library

Khan Academy has published the fastest typesetting library for the web. IntMath’s KaTeX and MathJax comparison demo shows some impressive performance improvements. The demo page took 177 ms to process on my laptop. The MathJax version on the other hand took 4777 ms. The performance comes at a price that not everything is supported in KaTeX (yet). I wish aligned equations were supported, but I can live with it. Until I run across more serious problems I’ll happily use KaTeX instead of MathJax.

How to stop a hanging Windows service

Windows processes and services can be controlled with the task manager, but occasionally I found hanging processes that required a reboot. Windows has some useful command line tools that could help avoiding a reboot and save some time: 1) Open command line prompt (cmd) as Administrator 2) Find process id with sc queryex {servicename}, e.g. sc queryex Apache2.4. You can also use tasklist|find "{executable}", e.g. tasklist|find "httpd" 3) Kill the process with taskkill /f /pid {PID}, e.


My first website used to be hosted on celephais.com, named after a short story by H.P. Lovecraft. I can’t believe it’s been 15 years now since I walked my first baby-steps on the web. I used the domain for a site dedicated to my favorite artists, musicians, authors, and movies - well, it was pretty much the unfinished sandbox of a site you’re looking at now, but built with static html files and a lot of graphics in a golden/brass 3d-look with lots of image maps.