Features & Capabilities

Balance a real inverted pendulum. 7 game modes, AI assistance, 100+ scientific metrics, Apple Health integration, and adaptive difficulty powered by your own biometrics.

The Pendulum is a rigorous inverted pendulum simulation built on real physics — not an approximation. Balance an unstable system using touch controls while the app tracks over 100 scientific metrics across your gameplay, health, and learning progress.

REAL PHYSICS, REAL CHALLENGE The simulation solves nonlinear differential equations in real time using a 4th-order Runge-Kutta integrator. Adjust mass, length, gravity, damping, spring constant, and moment of inertia to explore how parameter changes affect system dynamics. This is the same inverted pendulum problem studied in university control theory courses — now in your hands.

7 GAME MODES

  • Free Play: No levels, no timer. Balance at your own pace.
  • Progressive: Increasing balance duration with each level.
  • Spatial: The balance zone narrows as you advance.
  • Jiggle: Random perturbations shake the pendulum with increasing intensity.
  • Timed: Race against a countdown while maintaining balance.
  • Random: Physics parameters change unpredictably every level.
  • Golden Mode: AI-powered adaptive difficulty shaped by your Apple Health

AI ASSISTANCE Five AI modes let you learn, compete, or observe:

  • Off: Pure player control.
  • Helper: Gentle nudges when you're struggling.
  • Competition: The AI actively tries to destabilize you.
  • Tutorial: Step-by-step guided lessons with directional hints.
  • Demo: Watch the AI balance the pendulum to study optimal control.

100+ SCIENTIFIC METRICS Track your performance across six categories:

  • Basic: Stability, efficiency, session time, push count.
  • Advanced: Overcorrection rate, reaction time, directional bias.
  • Scientific: Phase space coverage, energy management, Lyapunov exponent.
  • Topological: Winding number, basin stability, periodic orbits, Betti
    numbers.
  • Educational: Learning curve slope, skill retention between sessions.
  • Performance: Frame rate, computation efficiency.

An interactive dashboard displays charts, time-filtered metrics, and health-performance correlations — all updating in real time.

APPLE HEALTH INTEGRATION Connect Apple Health to discover how your resting heart rate, HRV, sleep,
steps, and active calories correlate with gameplay performance. Sessions are
logged as mindfulness minutes. Golden Mode uses this data to adapt difficulty to your current physical and cognitive state.

CROSS-APP SYNERGY The Pendulum shares data with The Maze through a secure App Group connection. Balance control patterns combine with maze-solving cognitive metrics for a
unified picture of motor and mental performance.

BEAUTIFUL & CUSTOMIZABLE Choose from 9 nature photography themes — Acadia, Guatemala, Joshua Tree, Sachuest, New England, and more — or play on the default golden parchment. Toggle sound effects, haptic feedback, and control styles. Export all session data as CSV for your own analysis.

BUILT FOR EDUCATION & RESEARCH Suitable for physics coursework, nonlinear dynamics research, control theory demonstrations, cognitive science studies, and human-machine interaction experiments. Every metric is computed from first principles, not estimated.

10+ hand-crafted levels with infinite procedural generation beyond.

User Growth & Download Statistics

App
By:
Brian DiZio
Version:
1.1.0 Last updated: 2026-03-31
Version code:
883599951
Creation date:
2026-02-25
Compatible devices:
Size:
12.54MB
URLs:
Website ,Privacy policy
Full description:
See detailed description
Source:
Apple Apps Store
Data ingested on:
2026-06-07
Compare stats and ranking:

Contact the developer

Chrome-Stats does not own this Apple app. Please use these information below to contact the Apple app developer.
Developed by:
Brian DiZio
Apple Apps Store
https://apps.apple.com/fr/app/the-pendulum-2-0/id6758530419?l=en-GB
Website:
https://www.golden-enterprises.net

User Reviews

Está app es increíble!!! En entretenida además de que no tiene casi anuncios y además de que solo pesa 11 MB!! Me encanto esta app le doy un 10/10
by Bl*****, 2026-04-07

The controls are horrible and the game itself is unbalanced, unplayable
by Pl*****, 2026-04-06

Horrible on the ad they make it look so easy but when you play it its so bad it doesn’t balance or nothing and the controls are a bit hard to use and i keep restarting cause it doesn’t balance no matter how soft or hard i tap the buttons it doesn’t balance
by Li*****, 2026-04-05
View all user reviews ›

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