https://wljs.io/blog Tutorials, showcases, research notes, and developer updates from the WLJS Notebook community. en Wed, 05 Aug 2026 00:00:00 GMT https://wljs.io/blog/making-apps https://wljs.io/blog/making-apps A practical guide to building and deploying research applications with Wolfram Language and WLJS, covering interactive interfaces, asynchronous programming, physics, classical light-matter interaction, data import and export, and a complete Lorentz-oscillator fitting app. JerryI Wed, 05 Aug 2026 00:00:00 GMT tutorialmini-appresearchGUImegapost https://wljs.io/blog/music-1 https://wljs.io/blog/music-1 In this tutorial we start with the low-level `Sound` and `SoundNote` expressions used to describe playable audio, then move to the higher-level `Music*` framework introduced in WL 15 (Wolfram Engine 15). Stay in tune! JerryI Wed, 29 Jul 2026 00:00:00 GMT musicsound https://wljs.io/blog/sand-1 https://wljs.io/blog/sand-1 This post/notebook is a small side-view "falling sand" experiment. We start with the simplest material - sand. Each grain is one cell on a grid. A grain should fall if there is empty space below it, come to rest when blocked, and sometimes topple sideways when it is sitting in an unstable little stack. Those three behaviors are enough to make a recognizable pile 🏝️ JerryI Wed, 29 Jul 2026 00:00:00 GMT gamemodellingautomaton https://wljs.io/blog/fireflies-2 https://wljs.io/blog/fireflies-2 In this short post, we revisit [Fireflies, or Nature's Cellular Automaton](https://wljs.io/blog/fireflies) and recreate it with nothing more than scoped `Refresh` and a single external symbol. The notebook shows how surprisingly simple a coupled system can be when it is built from Wolfram Language primitives. JerryI Tue, 28 Jul 2026 00:00:00 GMT modellingsimulation https://wljs.io/blog/markov https://wljs.io/blog/markov Let's explore how Markov algorithms and Wolfram Language pattern matching can generate mazes, rivers, falling sand, and other cellular automata through simple rewriting rules. JerryI Mon, 15 Jun 2026 00:00:00 GMT algorithmstutorialautomaton https://wljs.io/blog/graphene-app https://wljs.io/blog/graphene-app A behind-the-scenes look at porting the Nanographenes Builder application to WLJS Notebook. The app helps researchers design nanographene hydrocarbons, analyze their molecular structures through graph-theoretical models, and experiment with new molecular configurations, while this tutorial explores reactive interfaces, event handling, asynchronous execution, and practical patterns for developing interactive Wolfram Language applications with WLJS. JerryI Mon, 08 Jun 2026 00:00:00 GMT GUImini-appchemistrytutorial https://wljs.io/blog/poll1 https://wljs.io/blog/poll1 We successfully tested the MCP server with our notebook interface on the development branch. We need your feedback on how to shape the future of the project. JerryI Mon, 27 Apr 2026 00:00:00 GMT poll https://wljs.io/blog/graphicscomplex2 https://wljs.io/blog/graphicscomplex2 The 3D story is the same - `GraphicsComplex` maps directly to THREE.js `BufferAttribute` objects written into GPU memory. The only difference is that you now also have `VertexNormals` for lighting. JerryI Sun, 26 Apr 2026 00:00:00 GMT graphicsGPUtutorial https://wljs.io/blog/graphicscomplex https://wljs.io/blog/graphicscomplex Ever wondered what happens when you push thousands of vertices into a graphics engine? `GraphicsComplex` can write directly into GPU buffers with no overhead. Let's see how far we can take it. JerryI Mon, 20 Apr 2026 00:00:00 GMT graphicsGPUtutorial https://wljs.io/blog/pid https://wljs.io/blog/pid This is one of the most widely used feedback control mechanisms. You will eventually find it everywhere, when you press the gas handle on an e-scooter, set the heater in your room, or even flush a toilet. JerryI Fri, 27 Mar 2026 00:00:00 GMT modellingphysics https://wljs.io/blog/squircle https://wljs.io/blog/squircle Do black dots look boring to you? Try [squircles](https://en.wikipedia.org/wiki/Squircle)! JerryI Sun, 22 Mar 2026 00:00:00 GMT graphicsutils https://wljs.io/blog/fireflies https://wljs.io/blog/fireflies Have you ever wondered how each firefly knows when to blink? How do they coordinate across the fields and trees? I guess we're heading towards a __many-body problem__ here. JerryI Sat, 21 Mar 2026 00:00:00 GMT modellingsimulation https://wljs.io/blog/timer https://wljs.io/blog/timer In this post we will use a notebook module for adding a "ghost" timer and discuss how you can organize your speaker notes. JerryI Tue, 17 Mar 2026 00:00:00 GMT presentationutils https://wljs.io/blog/cubes https://wljs.io/blog/cubes The [Marching Cubes algorithm](https://en.wikipedia.org/wiki/Marching_cubes) is a classic technique for extracting polygonal meshes from 3D scalar fields. In this notebook, we implement it as a C library via LibraryLink and render the resulting surfaces using plain `Graphics3D` with `GraphicsComplex`. The goal is to achieve real-time animation of isosurfaces - potentially thousands of polygons — with smooth shading powered by precomputed gradient normals. JerryI Mon, 16 Feb 2026 00:00:00 GMT C/C++geometryanimation3D https://wljs.io/blog/echo-tds https://wljs.io/blog/echo-tds It is common in time-domain spectroscopy to observe copies of the initial system response due to impedance mismatch. If deconvolution is not possible using slab-like models, then we have to smoothly suppress them to avoid artifacts in further processing JerryI Tue, 25 Nov 2025 00:00:00 GMT signal-processing https://wljs.io/blog/hypo https://wljs.io/blog/hypo Spirograph-like curves arise from simple sums of rotating vectors; a tiny tweak in frequency or phase yields striking patterns Refrigirator Sat, 11 Oct 2025 00:00:00 GMT animationmath https://wljs.io/blog/webcam https://wljs.io/blog/webcam In this example we will stream the data from your connected web-camera or any other camera-like device and perform real-time data processing JerryI Thu, 28 Aug 2025 00:00:00 GMT image processingIO https://wljs.io/blog/arduscope https://wljs.io/blog/arduscope An onboard ADC (analog-to-digital converter) is one of the basic features of Arduino-compatible boards. With just a few lines of code, the can turn voltages into numerical values. When streamed over a serial interface, these values let the Arduino act as a live external sensor-capturing data from photodiodes, microphones, or other circuits. JerryI Mon, 25 Aug 2025 00:00:00 GMT hardwareserialIO https://wljs.io/blog/goo https://wljs.io/blog/goo Here we shall try to model a system of interconnected bonds using the Verlet method. Then, we'll add some visuals to make it feel like a game. JerryI Fri, 22 Aug 2025 00:00:00 GMT physicsgamemodelling https://wljs.io/blog/billiard https://wljs.io/blog/billiard A toy-like example on the real-time collisions resolution using Verlet Integration method JerryI Thu, 21 Aug 2025 00:00:00 GMT physicscollisionsmodelling https://wljs.io/blog/verlet https://wljs.io/blog/verlet The Verlet method is one of the most elegant and simple numerical approaches to solving equations of motion. You can find it in molecular physics as well as in game development (cloth simulation). Recently, I made a [short video](https://www.youtube.com/shorts/6eLUQDEBBHI?feature=share) with a visual demonstration. JerryI Sun, 27 Jul 2025 00:00:00 GMT modellingphysicsanimation https://wljs.io/blog/drag https://wljs.io/blog/drag In this example, we construct a solid region with a Г-shaped cutout, where a small rectangle is going to be dragged by a user's mouse. JerryI Thu, 26 Jun 2025 00:00:00 GMT graphicsregionsinteraction https://wljs.io/blog/rim https://wljs.io/blog/rim Harnessing the power of Newton's equations and numerical methods to solve the dynamics of arbitrary planar meshes in real-time JerryI Thu, 01 May 2025 00:00:00 GMT modellingdifferencial equationsphysics https://wljs.io/blog/bandpass-app https://wljs.io/blog/bandpass-app A EQ-like band-stop filter mini app for processing any XY numerical data tables with interactive preview and real-time data manipulation. JerryI Mon, 24 Mar 2025 00:00:00 GMT signal-processingmini-app https://wljs.io/blog/keys https://wljs.io/blog/keys A notebook demonstrating a custom `View` functions with a working toy-like piano and guitar fingerboard. This covers basic graphics manipulation, sound emission and working with dynamic graphics groups. JerryI Mon, 10 Mar 2025 00:00:00 GMT musicgraphics https://wljs.io/blog/ppt https://wljs.io/blog/ppt An ultimate guide for non-WLJS/non-WL users. Programmatically generating slides and graphics isn’t new — you can already do it with Python, HTML, JSX, Julia, and more. Most tools combine declarative markup (like Markdown/HTML); we’ll take the same approach, but add dynamic elements, reusable components, and event bindings — all aimed at making things simpler, not harder. JerryI Sun, 02 Mar 2025 00:00:00 GMT guideslides https://wljs.io/blog/earth https://wljs.io/blog/earth Have you ever played Outer Wilds? The planets there are incredibly beautiful. This actually became the main motivation to create my own simple model of a planet, using real geographical elevation data and a bit of Wolfram Language magic. JerryI Wed, 08 Jan 2025 00:00:00 GMT animationmodellinggeo https://wljs.io/blog/glass https://wljs.io/blog/glass This code creates a magnifying glass effect over an image in Wolfram Language. As the mouse moves over the image, a zoomed-in circular region follows the cursor, simulating a magnifying lens. JerryI Wed, 01 Jan 2025 00:00:00 GMT graphics https://wljs.io/blog/units-app https://wljs.io/blog/units-app There are many physical units converters on the internet. Here we made one for our optics THz lab in University of Augsburg 🇩🇪 JerryI Thu, 12 Dec 2024 00:00:00 GMT mini-appphysics https://wljs.io/blog/raster https://wljs.io/blog/raster Thi basic animation creates an interference pattern by combining three sine waves with different frequencies JerryI Wed, 11 Dec 2024 00:00:00 GMT animation https://wljs.io/blog/diffraction https://wljs.io/blog/diffraction This post explores the basic computational analysis of Fraunhofer diffraction patterns using 2D fourier tranformation JerryI Mon, 25 Nov 2024 00:00:00 GMT opticsphysics https://wljs.io/blog/bar https://wljs.io/blog/bar You've likely seen videos featuring animated bar charts with a timeline, where the bars dynamically shift and overtake each other. Here is a snippet for that JerryI Wed, 11 Sep 2024 00:00:00 GMT animation https://wljs.io/blog/cov https://wljs.io/blog/cov By simply computing the covariance matrix and finding its eigenvectors and -values, you can determine the principal axes and the corresponding lengths of the ellipse JerryI Thu, 22 Aug 2024 00:00:00 GMT math https://wljs.io/blog/fluid https://wljs.io/blog/fluid In this post, we will explore a simple technique for simulating 2D incompressible fluids for visual effects. This work is mostly based on Jos Stam. Stable Fluids SIGGRAPH 1999 JerryI Wed, 21 Aug 2024 00:00:00 GMT physicsmodelling https://wljs.io/blog/fdtd https://wljs.io/blog/fdtd In this article, we attempt to solve Maxwell's equations for a 1D case with two interfaces. This work is based on John B. Schneider's Understanding the Finite-Difference Time-Domain Method, 2023 JerryI Mon, 15 Jul 2024 00:00:00 GMT researchopticsmodelling https://wljs.io/blog/fem https://wljs.io/blog/fem Here we will solve simple 2D wave-equation and visualize it in realtime using polygons JerryI Thu, 20 Jun 2024 00:00:00 GMT differential equationsmodelling3D https://wljs.io/blog/well https://wljs.io/blog/well Solving the time-independent Schrödinger equation for a **finite square quantum well** using numerical eigensystem methods. This notebook computes the first few bound-state energy levels and wavefunctions, and provides an interactive visualization. JerryI Sat, 08 Jun 2024 00:00:00 GMT quantum-physicsresearch https://wljs.io/blog/thz-tds https://wljs.io/blog/thz-tds Using a single Lorentz-Oscillator model we model the response of a materials with a variable thickness JerryI Mon, 20 May 2024 00:00:00 GMT researchopticsmodelling https://wljs.io/blog/gauge https://wljs.io/blog/gauge In this short post we code a gauge indicator in JS and integrate it with Wolfram Language JerryI Mon, 22 Apr 2024 00:00:00 GMT iojavascript https://wljs.io/blog/cl-1 https://wljs.io/blog/cl-1 An introduction guide on writting and testing compute shaders (GPGPU) written in OpenCL JerryI Mon, 01 Jan 2024 00:00:00 GMT openclGPU https://wljs.io/blog/fabrik https://wljs.io/blog/fabrik A very small and easy implementation of the Fabrik algorithm. Useful for animation, robotics or other optimization problems. JerryI Wed, 20 Dec 2023 00:00:00 GMT animationalgorithmsphysics https://wljs.io/blog/fitting https://wljs.io/blog/fitting Some primitives, as well as the entire canvas, can emit events on various user actions. Let's build an interactive Gaussian curve fit JerryI Sat, 09 Dec 2023 00:00:00 GMT graphics https://wljs.io/blog/spin-ham https://wljs.io/blog/spin-ham Today we delve into quantum mechanics with a focus on symbolic quantum operators and spin-Hamiltonians. It begins with setting up orthogonality rules and defining the linear properties of basis functions. JerryI Tue, 10 Oct 2023 00:00:00 GMT quantum-physicsresearch https://wljs.io/blog/rtx-old https://wljs.io/blog/rtx-old There is nothing more exciting in programming than designing a graphics application. We are happy to annouce that 3D plots now support realtime path-tracing. JerryI Thu, 20 Jul 2023 00:00:00 GMT devgraphics