Kirchhoff Arcade - Casual Physics

Kirchhoff Arcade is a hypercasual puzzle game that fuses Tetris-style stacking with real electric-circuit simulation. The falling pieces are electronic components — voltage sources, resistors, LEDs, conductive wires, and insulating blocks — that the player must fit onto a grid. When a piece locks into place, the game runs a full circuit analysis to determine whether a valid closed circuit was formed. Closing a circuit safely lights its LEDs and clears the components from the board; incorrect wiring, such as short circuits or over-current, burns the components and leaves debris behind.

A Note for Physics Enthusiasts

The game is a playful representation of Kirchhoff’s Laws and Ohm’s Law (I = V / R). Each locked piece is evaluated by a custom Modified Nodal Analysis (MNA) engine, which solves the circuit’s linear system and computes voltages and currents in real time. Components have real physical limits: LEDs light between 1 and 28 mA and burn out above that, resistors tolerate up to 50 mA, and sources short-circuit above 1 A. The LED is treated non-linearly, with a 2 V forward voltage drop and single-direction conduction — which is why reversed polarity genuinely prevents it from lighting.

Objective

The player must connect the falling components to form closed electric circuits. To light an LED safely, the correct polarity and a resistor to limit the current are required. The more components in a circuit, the higher the score — encouraging the player to build richer, more complex circuits.

Features

• Real Circuit Solver: Each locked piece is evaluated by a Modified Nodal Analysis (MNA) engine that solves the linear system via Gaussian elimination with partial pivoting, faithfully reproducing the board’s voltages and currents.
• Non-Linear LED Model: LEDs are solved iteratively with a 2 V forward-voltage drop and directional conduction, so reversed polarity genuinely prevents the LED from lighting.
• Physics-Based Outcomes: Components have real limits — LEDs light between 1 and 28 mA and burn out above it, resistors tolerate up to 50 mA, and sources short-circuit above 1 A.
• Component-Count Scoring: The score scales with the number of active components in a closed circuit, rewarding more complex circuits over trivial ones.
• Multiple Control Modes: Keyboard, on-screen virtual buttons, and touch gestures directly on the board (tap to rotate, drag to move, swipe down to drop).
• Persistence: The high score is automatically saved in the player’s browser via localStorage.
• Responsive and Multilingual: Fully optimized for desktop and mobile browsers, with automatic language detection and native support for Portuguese and English.

Scores and Skill Levels

Your classification in the game is defined by your all-time high score:

• < 1000: Beginner ⚡
• 1000 – 1999: Student ⚡
• 2000 – 2999: Technician ⚡
• 3000 – 3999: Engineer ⚡
• 4000+: Kirchhoff ⚡
  

How to Play

• Objective: Connect the falling components to form closed electric circuits. To light an LED safely, use the correct polarity and a resistor to limit the current.
• Challenges: Never wire a source’s (+) pole straight to its (−) — this causes a short circuit. Higher voltages need bigger resistors; when unsure, prefer the 470 Ω. Closing a circuit next to burned debris or insulating blocks also clears them from the board.
• Controls:

💻 On PC:

• [ ← ] / [ → ] : Move the piece left or right.
• [ ↑ ] : Rotate the piece.
• [ ↓ ] : Speed up the fall (soft drop).
• [ Space ] / [ Enter ] : Instant drop (hard drop) / confirm the circuit result.
• [ R ] : Restart the game.

📱 On Mobile / Touch:

• On-screen buttons: a directional pad (left, rotate, right, down) plus a large DROP button.
• Gestures on the board: tap to rotate, drag sideways to move, swipe down for a hard drop.

Change Language

You can switch between Portuguese and English by clicking the language button on the main menu screen. The browser language is automatically detected on the first visit.

Author

This project was developed by:

Prof. Dr. Rafael João Ribeiro Federal Institute of Paraná (IFPR) www.fisicagames.com.br

Copyright © 2026 Rafael João Ribeiro.