Rendering the Mandelbulb
Learn how to render a fully interactive Mandelbulb fractal in WebGL, from the math and ray marching to shading, soft shadows, and depth of field.
Projects
CSR2
Natural Motion
Setting a new standard in visuals, CSR 2 delivers hyper-real drag racing to the palms of your hands. Compete against live players across the world with your custom built supercars including LaFerrari, McLaren P1™, Koenigsegg One:1 and many more.
Pokémon Art Academy
Kuju / Headstrong Games
Pokémon Art Academy is an educational drawing video game developed by Headstrong Games and published by Nintendo for the Nintendo 3DS. It is a spin-off of the Art Academy series featuring characters from the Pokémon media franchise.
VBS Tactics
Bohemia Interactive Simulations
VBS Tactics allows users to conduct real-time tactical exercises up to the company level. Its intuitive interface can be used to configure doctrine-based orders of battle, plan a mission, execute it in real time, and review the results in after-action review.
Samsung S10 AR Emoji
Samsung Electronics
The new version of the AR Emoji is released with the Samsung Galaxy S10 range of devices. Samsung's avatars are integrated in the camera app and allow the user to create a virtual presence character that is adopted to their own characteristics.
XTracer
Personal Project
An experimental offline renderer based on path tracing.
GoveeWatch
Personal Project
A curses application that picks up bluetooth broadcasts from Govee thermometer / hydrometer devices and displays readings at real-time.
Gameboy Snake
Personal Project
A Nokia Snake inspired game built for the Nintendo Game Boy, written entirely in GBZ80 assembly.
Asciimg
Personal Project
Asciimg is a small utility that allows displaying images in a command line terminal.
Blog
Building a Hamiltonian path puzzle
Number Trail is a Hamiltonian-path puzzle: draw one continuous line that visits every cell exactly once, passing through numbered clues in order. This post goes over the implementation from puzzle file format to board rendering, drag controls, and Warnsdorff's random generator.
Haversine Distance
The haversine formula computes the great-circle distance between two points on a sphere from their latitude and longitude. It is simple, fast, and accurate enough for many mapping and location tasks.
Pale Blue Dot
A reflection on Voyager 1's Pale Blue Dot image, Carl Sagan's moral vision, and why that distant photograph still matters today.
The Gaia Database
A practical introduction to the Gaia database and its major data releases. Includes a simple ADQL example and a guide to parallax, epochs, and key data fields.
Mulberry32: A Tiny, Fast, Deterministic RNG
A detailed guide to the ubiquitous Mulberry32 pseudo-random number generator. I go over the theory and include a complete implementation, with deterministic seeding, and practical helper utilities.
Reaction-Diffusion: Gray-Scott on a 2D Grid
A detailed breakdown of the Gray-Scott reaction-diffusion algorithm. Includes an interactive canvas demo and explains the PDE model, Laplacian stencil, double buffering, and boundary handling.
Raindrops on a puddle
A breakdown of a two-pass shader technique that simulates realistic water ripples from falling raindrops using wave propagation and ray marching to render an interactive puddle with reflections.
Game Boy port of Snake in Assembly
A port of a classic Snake game for the Nintendo Game Boy, written in GBZ80 ASM. Covers the state machine, snake ring buffer, occupancy grid collision detection, and VBlank-safe rendering.
A Universe Without Time
A layman's guide to Julian Barbour's timeless view of reality, including Nows, time capsules, Machian dynamics, shape dynamics, and the Janus point, plus how the scientific community responds.
Seestar ALP Launcher
I wrote two small shell scripts that make Seestar ALP + INDI painless on Debian. They create a venv, install deps, apply the pyINDI indi.dtd fix, clone or update upstream, then run a full INDI session.
A Guide to using the useEffect hook in React
A practical guide to React useEffect, when to avoid it, common pitfalls, and how cleanup works.
RTSP camera streaming with Raspberry-Pi Zero 2
A clean, reliable way to stream a Raspberry Pi Zero 2 CSI camera over RTSP on a headless setup, focusing on a simple configuration that’s easy to maintain. You’ll get the basics needed to bring the stream up and view it remotely with a headless setup.
ASCII Fire
The classic fire effect, rendered with ASCII characters. Heat values are seeded at the bottom, and then propagated upward through neighbor averaging, and mapped to characters and colors to create animated flames.
Ray marching a blob
A deep dive into rendering animated metaballs (aka blobs) with ray marching, PBR shading, shadows, and CPU driven simulation in WebGL and Three.js.
Random Mutation Hill Climbing (RMHC)
An exploration of how we approximate an image using an evolutionary strategy. One candidate, one mutation, accept if better. We climb the fitness landscape in real time with frame-budgeted rendering and converge on surprisingly good results.
Triple Buffering in Rendering APIs
A practical guide to triple buffering, how it improves smoothness and throughput over double buffering, when to use it, and how to wire it up in modern APIs.
Rendering the Mandelbulb
A deep dive into rendering the Mandelbulb fractal in WebGL using ray marching, distance estimation, orbit traps, and advanced shading techniques. We’ll explore the math, shader implementation, and how fractals like the Mandelbulb inspire cinematic visuals.
Implementing a foil sticker effect
A breakdown of how to build a custom Three.js shader that recreates the iridescent, sparkling look of foil stickers using vertex deformation, angle-based color shifts, and procedural flakes.
Redshift: The Cosmic Fingerprint of Light in Motion
Light stretches as it travels, shifting redward and revealing motion, distance, and even the chemistry of galaxies like record-breaking JADES-GS-z14-0
Polaris: The Celestial Anchor of the North
Polaris, has guided humanity for centuries thanks to its unique position in the night sky. This bright supergiant star serves as a reliable navigation aid, a symbol across cultures, and an intriguing triple star system studied by astronomers.
Understanding Unity’s Render Pipelines
Unity’s render pipelines, Built-in, URP, HDRP, offer different trade-offs in performance, visuals, and flexibility. Learn how they work, when to use each, and how to extend them with Command Buffers, Render Features, and Custom Passes.
The Andromeda Paradox
A slow walk on Earth can shift our view of what’s happening right now in a galaxy millions of light-years away. The Andromeda Paradox illustrates how special relativity warps our sense of simultaneity.
NGC6960: The Veil Nebula
A brief report in my latest astrophotography session, where I captured NGC6960, also known as the Veil Nebula.
A condensed guide to React hooks
A quick reference guide to React hooks. When to use useState, useEffect, useRef, useMemo & more. Includes comparison tablew, real examples, and common gotchas to look out for.
Simulating the Seestar S50 in Stellarium
Learn how to set up the Seestar S50 smart telescope in Stellarium using accurate sensor and telescope parameters. This guide covers both standard and 2x mosaic modes to help you simulate your field of view for better astrophotography planning.
The MRS Fractal: Mirror, Rotate, Scale
A practical implementation of the MRS fractal technique, a simple iterative transform built from mirror, rotation, and scale operations.
Reviving the classic RTS “Z” with DOSBox
A step-by-step guide to setting up DOSBox on Linux to play the classic RTS game Z by Bitmap Brothers using your original game ISO.
Generating audio transcripts
This short write-up offers a quick overview of a simple method you can use to create a transcript from either a video or an audio file, which may be helpful in a variety of contexts such as documentation, content analysis, or accessibility.
Game Frame Breakdown Articles
A curated list of technical articles that reverse-engineer and dissect how video games render a single frame, covering geometry, lighting, shadows, post-processing, and more.
Implementing a todo app, Part 1: The Backend
Part 1 of a blog post series on full stack development, where I walk through the process of building a simple task management app. This chapter focuses on implementation of the backend services.
Speech synthesis for web applications
I've introduced a feature that lets you listen to my blog's content being read aloud. This post explains how I implemented it using the Speech Synthesis Web API, which requires minimal code and works on most modern browsers.
Gameboy Development, Part 1: Hello World!
A step-by-step guide for creating a 'hello world' ROM for the Nintendo Gameboy in assembly
Working with encrypted file archives
A brief guide on encrypting and decrypting tar archives with gpg
ZEXMTE BT-506 in Debian
A guide on how to make the ZEXMTE BT-506 dongle work in Debian
Notifications Using Telegram
A tutorial on using telegram to generate notifications
Docker in Debian
Notes on using Docker in Debian
Getting creative with asciimg
A fun experiment in using text to render animated images in a terminal
Lossy Compression of Unsigned Float Numbers
Notes on a lossy unsigned float number compression technique
Shadow Mapping
This article introduces shadow mapping, a technique for creating shadows in graphics. It explains how to capture depth from the light’s view to find shadowed areas and outlines basic steps to implement it, including making and using shadow maps.
Peripage bluetooth printing via the terminal
A tutorial on interfacing a peripage printer via the command line
Using Yubikey FIDO2 to login in Debian/GDM
A brief guide on using Yubikey as an authentication method with GDM
Intel's Panel Self Refresh (PSR) Feature
A brief guide on resolving Intel's PSR issues
Midjourney
A brief post on generating images with Midjourney
Brachiograph plotter
Brief notes on building a brachiograph plotter
Normal Map Blending
A brief survey of normal blending techniques
Notes on Unreal Engine 5, Nanite
Nanite in UE5 is a virtualized geometry system that renders only visible detail, enabling film-quality assets with millions of polygons and minimal performance cost. It replaces normal maps, supports dynamic LODs, and uses a hybrid rasterizer for optimal efficiency.
Reviving old software to run on a modern machine
A short case study on how to bring old software back to life
Creating floppy disk images in Linux
A short guide on creating floppy disk images in Linux
The De Moivre theorem
Theory and implementation of the De Moivre theorem
Macro-Photography with a Mobile Phone (Part 2)
Another way to turn your mobile phone into a macro camera
Macro-Photography using a Mobile Phone
A simple way to turn your mobile phone into a macro camera
Classic Demo Effects, Twister
The classic demoscene effect explained and implemented in GLSL
Irradiance, Spherical Harmonics
Spherical Harmonics are a type of Spherical Radial Basis Function that can be used to encode signals defined on a sphere in a compact way. This makes them an excellent fit for encoding a variety of datasets commonly used in real time graphics."
Irradiance, Ambient Cube
In Half-Life 2, a directional ambient term is precomputed across the environments and stored in the ambient cube lighting encoding. This post goes over the theory behind the ambient cubes technique and presents an implementation in GLSL.
Generative art
Generative art is an algorithmic approach to creating unique and dynamic works of art. As technology progresses, it continues to evolve, allowing artists to explore new forms and patterns beyond traditional methods.
Full Screen Pass Without Explicit Geometry
A brief explanation on how to render a full screen pass efficiently in OpenGL and DirectX
Elementary Cellular Automaton, Rule 126
Wolfram's infamous rule 126 explained in plain terms
Classic Demo Effects, Fire
The classic demoscene effect explained and implemented in GLSL
OpenGL Geometry
A brief survey of various ways OpenGL can draw geometry
Half-Space Test
An explanation of the math behind half-space testing
Distributed Ray-Tracing
An overview of how distributed ray-tracing enhances realism by addressing the limits of traditional ray-tracing, using Monte Carlo sampling to simulate effects like soft shadows, gloss, depth of field, and motion blur.
Historical Computer Generated Animations
A listing of CGI films, that played a pivotal role in the history of computer graphics
Lindenmayer Systems
L-Systems are a mathematical framework for modeling organic structures and fractals. They generate complex patterns and are used in graphics, biology, and procedural generation. In this blog post I share some examples and how to implement them.
Interpolation Methods
A collection of useful interpolation methods, theory and implementation
Optical Illusions, Lightness Constancy
Lightness constancy allows us to perceive surface brightness as stable despite changes in lighting. The Checker Shadow Illusion highlights how context, shadows, and spatial cues trick the brain into seeing identical shades as different.
BTRFS, Quick Start
A brief guide on using BTRFS
Useful Functions for Graphics
A listing of useful math formulas and their plots
Generating Stereo Anaglyphs with ImageMagick
How to generate stereo anaglyphs with ImageMagick
Raytracing, Ray-Plane Testing
Ray to Plane intersection testing, theory and implementation
Sampling a Disk, Vogel's Method
There are many ways to spread points across the surface of a disk but doing so in an even distribution can be challenging. Vogel’s method solves that problem elegantly. In this blog post, I explore the underlying math and show how to implement it.
Visibility Culling
A listing of visibility culling techniques
Sprite Encoding / Decoding Using Literals
A simple approach for sprite texture encoding
Edge Detection Using the Sobel Operator
The Sobel operator explained and implemented in GLSL
Matrices: From Linear Algebra to Graphics
NOT SET
Color Grading, An Artist Driven Approach
A simple method of implementing color grading
Plasma Effect
The classic plasma effect is a staple of demoscene history. Using sinusoidal functions and color gradients, it creates mesmerizing organic patterns that flow and pulse across the screen.
Law of Reflection
The physics law of reflection, theory and implementation
PostFX, Pixelize
Implementation of pixelization effects in GLSL
Anti-Aliasing, FXAA
A high level explanation of FXAA and how to implement it in GLSL
NCF, A Minimalistic Meta-Language
A short guide on NCF specification and how to use it in your own projects
Metaballs
Metaballs, what are they and how to make them
Pseudo 3D Tunnel Effect
The classic demoscene effect explained and implemented in GLSL
From Geometric to Coordinate Form: Understanding the Dot Product
This post shows how the geometric dot product, lengths times cosine of the angle, can be converted into the coordinate form by summing the products of corresponding components, proving both forms are equivalent.
Conway's Game of Life
A GPU implementation of Conway's game of life
Fractals, Mandelbrot & Julia Sets
Theory and GPU implementation of the Mandelbrot and Julia fractal sets
C/C++ Embedded Files
A summary of different approaches for embedding files within c / c++ code
Primus Under Debian/Sid
A short guide on enabling and using Primus under Debian Sid
GNU Make, Parallel Processing
Parallel processing with GNU Make
No posts match your search.
Publications
Sena, D.B.M., Papadopoulos, N. and Gkountis, A., Samsung Electronics Co Ltd, 2019. Method for estimating light for augmented reality and electronic device thereof. U.S. Patent Application 16/409,083.
Sousa, N.; Sena, D.; Papadopoulos, N. and Pereira, J. (2019). Acceleration Data Structures for Ray Tracing on Mobile Devices.In Proceedings of the 14th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 1 GRAPP: GRAPP, ISBN 978-989-758-354-4, ISSN 2184-4321, pages 332-339. DOI: 10.5220/0007575403320339
Abstract
Mobile devices are continuously becoming more efficient at performing computationally expensive tasks, such as ray tracing. A lot of research effort has been put into using acceleration data structures to minimize the computational cost of ray tracing and optimize the use of GPU resources. However, with the vast majority of research focusing on desktop GPUs, there is a lack of data regarding how such optimizations scale on mobile architectures where there are a different set of challenges and limitations. Our work bridges the gap by providing a performance analysis of not only ray tracing as a whole, but also of different data structures and techniques. We implemented and profiled the performance of multiple acceleration data structures across different instrumentation tools using a set of representative test scenes. Our investigation concludes that a hybrid rendering approach is more suitable for current mobile environments, with greater performance benefits observed when using data structures that focus on reducing memory bandwidth and ALU usage.
Creative Writing
A Longhouse of Ravens
A Norse warrior wakes on a battlefield next to the frozen dead. He begins a journey to reunite with his tribe. Each step brings him closer, and costs him more, until the world he thought he knew comes undone.
Mother
In a besieged underground world, a low-caste laborer serves the unseen Mother through hunger, collapse, and a war that does not distinguish the living from the useful.
The Synod of the Veil
In a society where doctrine shapes daily life, devotion functions as both faith and civic compliance. A dutiful analyst follows every rule until the same system that promises order begins to address him with unsettling intimacy.
One last delivery
A retired postman’s quiet routines begin to unravel when messages that refuse to stay in the past start appearing at his door, each delivery sharpening into a pattern that feels less like coincidence and more like a reckoning.
Contamination
A recurring signal is uncovered in decades-old archives and filed as noise. Years later, it appears again in live sky data, first as a technical anomaly and then as a pattern no instrument can dismiss.
Contents Not Disclosed
Out of work and desperate, Daniel takes a no-questions courier gig: pick up a sealed box from an abandoned warehouse and deliver it by dawn. But the night keeps its own rules, its own voices, and a route that won’t bring him back unchanged.
Artifact 12
A journalist arrives at a wealthy collector’s estate to carry out an exclusive interview. Inside, the tour slides from questions to exhibits. Meanwhile, the house quietly imposes its own order, and observation turns into participation.
The room
A restless occupant wakes in a room that seems to remember more than they do. Between stillness and hesitant motion, they test how long they can live beside an unnamed absence before it quietly defines who they are.
The Hollow Light Within
In a sun-scorched world, the earth lies in ruin. A scavenger on a mission discovers a mysterious sanctuary, and ignites a chain of events that could reshape what remains of the world.
Somewhere Else
Nathan Caldwell has it all: success, a beautiful home, and a loving family. But today is no ordinary day. What unfolds will push him to the edge and change everything.
Artwork
I create art through mathematics and code, driven by a deep appreciation of fractals, science, and the hidden structures of nature. Every artwork is built entirely from scratch using my own rendering engine, sculpted through equations and iteration until the simulation reveals something extraordinary and beautiful. The same recursive logic that carves a coastline, unfurls a fern, or spirals a galaxy finds its way onto the canvas through pure mathematics. No filters, no brushes. Only algorithms, curiosity, and an obsession with the infinite.
Thank you for wandering this far,
Bronze Fractal Heart
A Julia fractal rendered in luminous bronze, where mathematical precision unfolds into a form that feels unmistakably organic. Its swirling contours and intricate textures evoke natural growth, carved wood, flowing tissue, and even the silhouette of a heart. A structure born from equations, yet resonant with the living patterns of nature.
Azure Infinity
Azure Infinity transforms the Menger sponge fractal into a calm, architectural sculpture of depth, repetition, and infinite structure. Rendered in soft blue tones, the form reveals how mathematics can create beauty through pure logic alone; each opening leading deeper into a pattern that repeats across scale.
Nocturnal Tide
Deep navy and icy blue currents sweep across like waves moving under moonlight. Nocturnal Tide captures motion, mystery, and quiet energy, blending oceanic depth with sleek abstract elegance.
Published Games
Snake
Released Price Name your own price
Version 0.2.1
Size 32 kB
Platform Game Boy
A classic Snake clone for the original Nintendo Game Boy, written entirely in GBZ80 assembly. It runs as a proper Game Boy ROM with tile-based rendering, simple controls, and the familiar constraints of 8-bit handheld hardware.
© 2012 - 2026, Nikolaos Papadopoulos. All Rights Reserved.
No part of this work may be reproduced or transmitted without the prior written permission of the author.