The following Vibe Coding single page web applications are built using AI and run on most web
                browsers and mobile
                devices.
            
            
                "Vibe coding" is a term coined by Andrej Karpathy in early 2025 to describe a conversational and
                intuitive
                approach to programming using AI tools, particularly large language models (LLMs).
            
        
            Introduction to symbolic AI
            
        To be continued ...
            Introduction to stateless vector AI
            
                 The simplest AI imaginable with just one neuron
                The simplest AI imaginable with just one neuron
                
            
                 Curve fitting a workhorse of modern AI
                Curve fitting a workhorse of modern AI
                
            
                 Gradient Decent vs. Simulated Annealing
                Gradient Decent vs. Simulated Annealing
                
            
            
         The simplest AI imaginable with just one neuron
                The simplest AI imaginable with just one neuron
                Learn the basics of AI and experiment with a neural network consisting of a single neuron,
                    optimize parameters and experience how AI algorithms develop in real time.
                    Perfect for anyone who wants to understand the fundamentals of AI,
                    from aspiring data scientists, tech enthusiasts to average joe.
                
             Curve fitting a workhorse of modern AI
                Curve fitting a workhorse of modern AI
                
                    Most people associate human-like machines that can see, speak and reason with brain-like neural
                    networks
                    that can think and reflect on a problem.
                
                
                    But Artificial Neural Networks (ANNs) are mostly stateless and primarily master one thing: they
                    excel at
                    curve fitting, mapping input data to outputs through complex functions, enabling them to solve
                    diverse
                    problems, including training large language models (LLMs).
                
                
                    Let’s now demystify this core concept of modern AI
                
                
             Gradient Decent vs. Simulated Annealing
                Gradient Decent vs. Simulated Annealing
                This software demonstrates the solution to an optimization problem, using the example of the
                    shortest
                    route to a hospital. Optimization problems play a central role in machine learning.
                
            To be continued ...
            Stateful AI
            
                 Hopfield / Boltzmann Network Simulation
                Hopfield / Boltzmann Network Simulation
                
            
         Hopfield / Boltzmann Network Simulation
                Hopfield / Boltzmann Network Simulation
                
                    The 2024 Nobel Prize in Physics was awarded to John J. Hopfield and Geoffrey Hinton for their
                    foundational work in artificial neural networks, which includes Hopfield networks and Boltzmann
                    machines. Their contributions have been instrumental in advancing machine learning and AI.
                
                This simulation shows an energy-based neural network that is similar in function to Hopfield and
                    Boltzmann networks.
                
            To be continued ...
            Large Language Models
            
                 LLMs Part 1: Understand the meaning of words through AI
                LLMs Part 1: Understand the meaning of words through AI
                
            
                 LLMs Part 2: Understand token position through AI
                LLMs Part 2: Understand token position through AI
                
            
                 LLMs Part 3: Understand long context through AI
                LLMs Part 3: Understand long context through AI
                
            
                 LLMs Part 4: Put the pieces together. The simplest LM imaginable
                LLMs Part 4: Put the pieces together. The simplest LM imaginable
                
            
            
         LLMs Part 1: Understand the meaning of words through AI
                LLMs Part 1: Understand the meaning of words through AI
                
                    This AI embedding algorithm
                    visualizes the relationships and meanings of words in a 2D vector space,
                    where every word tells a story through its position and connections.
                
                
                    This deep comprehension of word meanings forms the basic building block for large language models
                    (LLMs),
                    enabling them to generate coherent, contextually relevant text.
                
                
             LLMs Part 2: Understand token position through AI
                LLMs Part 2: Understand token position through AI
                
                    Unlike traditional sequence models like Recurrent Neural Networks (RNNs), which process tokens
                    sequentially,
                    Transformers process all tokens in parallel and thus lack an inherent understanding of token order.
                
                
                    Positional encoding addresses this challenge by encoding positional information into the token
                    embeddings.
                
                
             LLMs Part 3: Understand long context through AI
                LLMs Part 3: Understand long context through AI
                
                    The attention mechanism revolutionized NLP by enabling models to focus on important parts of the
                    input
                    sequence,
                    allowing for contextually accurate responses even in long sequences.
                
                
                    Introduced in the 2017 paper "Attention Is All You Need" by Vaswani et al., self-attention has
                    become a
                    cornerstone of
                    modern AI and the transformer architecture of LLMs.
                
                
             LLMs Part 4: Put the pieces together. The simplest LM imaginable
                LLMs Part 4: Put the pieces together. The simplest LM imaginable
                
                    Let us now demystify the intricacies of Large Language Models (LLMs) and bring theory to life with
                    an interactive simulation.
                
                
                    Watch in real-time as this basic yet fascinating transformer model runs a live simulation,
                    piecing together language constructs with the elegance of simplicity.
                
                
            To be continued ...
            AI use cases
            
        To be continued ...
            Science WebApps
            
                 Real-time FFT Spectrum and Spectrogram Analyzer
                Real-time FFT Spectrum and Spectrogram Analyzer
                
            
                 3D Gas Simulation
                3D Gas Simulation
                
            
                 3D Solar System Simulator
                3D Solar System Simulator
                
            
                 Archimedean Screw Turbine
                Archimedean Screw Turbine
                
            
                 3-Phase Generators in the grid
                3-Phase Generators in the grid
                
            
                 Simulation of coupled Pendulums and Emergent Synchronization
                Simulation of coupled Pendulums and Emergent Synchronization
                
            
         Real-time FFT Spectrum and Spectrogram Analyzer
                Real-time FFT Spectrum and Spectrogram Analyzer
                
                    Analyze audio signals effortlessly with this web-based tool.
                    Visualize the frequency spectrum and spectrogram of MP3 files or live input from
                    your microphone in real time, all within your browser.
                    Ideal for uncovering sound details with precision and ease.
                
                
             3D Gas Simulation
                3D Gas Simulation
                The 3D gas simulation shows particles in a 3-dimensional space that meet and repel each other
                    depending
                    on the temperature. The energy distribution is shown as a diagram.
                
             3D Solar System Simulator
                3D Solar System Simulator
                Immerse yourself in a streamlined 3D animation of the solar system, where planets and moons are the
                    stars of the show. Glide effortlessly through the vast reaches of space in fly mode, weaving through
                    the
                    orbits of planets. Marvel at their sizes and positions as you soar past Earth, skim the colossal gas
                    giants, and venture into the outer regions.
                
             Archimedean Screw Turbine
                Archimedean Screw Turbine
                
                    Explore hydropower dynamics with our Archimedean Screw Turbines Simulation.
                    Customize turbine designs by adjusting blade numbers and inclination angles,
                    and visualize the impact of design parameters.
                
                
             3-Phase Generators in the grid
                3-Phase Generators in the grid
                
                    This simulation provides a detailed visualization of how two 3-phase generators operate, producing
                    synchronized sine waves that ultimately merge into the larger grid waveform. It illustrates key
                    electrical principles such as phase alignment, frequency synchronization, and waveform
                    superposition—offering a compelling demonstration of real-world power generation dynamics.
                
                
             Simulation of coupled Pendulums and Emergent Synchronization
                Simulation of coupled Pendulums and Emergent Synchronization
                
                    This simulation beautifully illustrates the synchronization phenomenon first observed by Christiaan
                    Huygens
                    in the 17th century. Huygens discovered that two pendulum clocks mounted on the same beam would
                    eventually
                    synchronize their swings due to subtle forces transferred through the shared structure.
                
                
            To be continued ...
            Data WebApps
            
                 US Trade Balance Map
                US Trade Balance Map
                
            
         US Trade Balance Map
                US Trade Balance Map
                
                    Explore the United States international
                    trade with this interactive map.
                
                
                    Hover over each nation to instantly see the balance of trade,
                    clearly indicating whether the US has a trade surplus (exporting more than importing)
                    or a trade deficit (importing more than exporting).
                
                
            To be continued ...
            Tool WebApps
            
                 LineBreak Designer
                LineBreak Designer
                
            
                 Compound Interest Calculator
                Compound Interest Calculator
                
            
                 Web Synthesizer
                Web Synthesizer
                
            
         LineBreak Designer
                LineBreak Designer
                This tool is designed to refine text formatting.
                    Users can input text into a resizable text area, adjusting paragraph width seamlessly with mouse
                    interaction.
                    The app will then create precise line breaks for the given text area width.
                
                
             Compound Interest Calculator
                Compound Interest Calculator
                Compound Interest Calculator shows the capital development over a specified time and interest rate.
                
                
             Web Synthesizer
                Web Synthesizer
                
                    Transform your browser into a powerful music studio with our vibe coded web synthesizer! This
                    intuitive tool lets you craft rich, dynamic sounds effortlessly. Tweak parameters in real time, and
                    design your own unique soundscapes—all without downloading software.
                
                
            To be continued ...
            Animation WebApps
            
                 Bouncing Ball (ASMR) animation
                Bouncing Ball (ASMR) animation
                
            
         Bouncing Ball (ASMR) animation
                Bouncing Ball (ASMR) animation
                
                    Experience the mesmerizing charm of a bouncing ball that
                    shifts through a spectrum of vibrant colors.
                    This ASMR simulation combines rhythmic motion with a dynamic visual display,
                    as the ball gracefully bounces and transforms its hues with every impact.
                
                
            To be continued ...
            Covered AI topics
            
        
    Vibe coding
                "Vibe coding" is a term coined by Andrej Karpathy in early 2025 to describe a conversational and
                intuitive
                approach to programming using AI tools, particularly large language models (LLMs).
            
            Search AI systems excel at retrieving information quickly
                and
                efficiently, whether from
                databases or the web.
            
            NLP Understanding the meaning and context of language
                and data is crucial for tasks like
                natural language processing, enabling machines to understand, interpret, and generate human language.
            
            Compression Reducing the size of data while preserving
                important information is key for
                efficient storage and transmission.
            
            Planning AI can develop strategies and plan actions to
                achieve
                specific goals, particularly in
                robotics and game playing.
            
            Optimization AI algorithms often seek to find the best
                solution to a problem, whether it's
                minimizing costs or maximizing efficiency.
            
            Approximation AI models approximate complex functions and
                patterns in data, allowing for
                predictions and decision-making.
            
            Logical Reasoning AI can apply logical rules to draw
                inferences and make decisions based on
                available information.
            
            Perception AI systems process sensory information, such as
                visual, auditory, and tactile data,
                to understand and interpret the world. This is crucial for tasks like image recognition and speech
                processing.
            
            Learning AI can adapt and improve from experience through
                various learning methods, such as
                supervised, unsupervised, and reinforcement learning. This capability is essential for tasks like
                pattern
                recognition and predictive analytics.
            
            Interaction AI involves communication with humans or other
                systems through natural language
                processing, dialogue systems, and user interfaces. This is key for applications like virtual assistants
                and
                customer service bots.
            
        