Computer Programming

Cellular Automata (CA) on 3D Lattices

Some interesting images from the project

This project was made in the Wolfram Language as part of the Wolfram Summer School 2020. The aim was to run Cellular Automaton on 3D lattices. There were two ways to approach the problem. The first was to work with the parallelepiped unit cells defined by the basis vectors of the lattice. This is very similar to running CA on a cubic lattice (in terms of the neighbourhood structure and the rules). The second (and the more interesting) was to run CA on the lattice points themselves, which required working with the Voronoi regions around the points. Visit my Wolfram Community Post published on the Wolfram Community Blog for details.

Simulating Surface Water Waves

The above videos are simulations in Python using pyqtgraph library. They were made as part of the internship at the Institute of Science and Technology in Austria. The first video is for a wave packet following dispersion relation of a free particle given by the Schrodinger equation. The second video is for surface water waves given by the deep water dispersion relation. Click here for more details.

Wolfram demonstrations:

Spread of a Gaussian Wave Packet with Time: https://demonstrations.wolfram.com/SpreadOfAGaussianWavePacketWithTime/
Kepler Orbits: https://demonstrations.wolfram.com/KeplerOrbits/
Fraunhofer Diffraction Through a Rectangular Aperture: https://demonstrations.wolfram.com/FraunhoferDiffractionThroughARectangularAperture/

The above projects are computer simulations made in Mathematica language and have been published on the Wolfram Demonstrations Project page. These aid in the visualisation of the Physics concepts involved.

Normal Numbers

[slideshare id=234034213&doc=normalityofpi-200515104536]

This project (made in Python) explores normal numbers, in particular, $\pi$ , $e$ and $\sqrt[]{2}$ in different bases (decimal and hexadecimal).

Square Wheel

This is a computational project made using C++. A circular wheel has been one of the greatest inventions of manking. It rolls perfectly well on a flat ground. What if we consider polygonal wheels? A square wheel would not “roll smoothly” on a flat road. A smooth ride with square wheels is possible on an inverted catenary. The project demonstrates animation of a smooth ride using square wheel.

Fractals

mandel3 — Click to know more about **FRACTALS**

For my CBSE class 12 project, I made a program for generating various types of fractals and tracking the trajectory of points. The code also had the feature for zooming in and changing various initial conditions and storing the data obtained.

Finding value of pi by Monte Carlo method

[slideshare id=54202514&doc=s79tz7dfrsskqjrshjzm-signature-c1e3f6593d7f230f8e93a342635c2cbd0f8db44d5aac7a2734c7e0ee8f5edcc2-poli-151021065413-lva1-app6892&type=d]