GPT-4o vs. Gemini: AI Models Tested with Physics Simulation

How well do AI models solve complex coding tasks? We tested GPT-4o, GPT-4o-mini, Gemini 2.0, and Gemini 1.5 Flash on a Multi-Ball Physics Simulation. Flagship models excelled, while lighter versions highlighted trade-offs between speed and precision. Read on for insights into their performance and capabilities.

Language models like OpenAI’s GPT-4o and Google’s Gemini have become essential tools for coding, problem-solving, and automating complex tasks. For this test, we focused on their widely used standard models—GPT-4o, GPT-4o-mini, Gemini 2.0, and Gemini 1.5 Flash—rather than their flagship versions. These standard models are faster, more cost-efficient, and more practical for real-world applications where speed and scalability often outweigh the need for cutting-edge complexity.

The Task: Multi-Ball Hexagonal Simulation

The models were tasked with generating Python code for a physics simulation involving three balls of different sizes and weights inside a static hexagonal arena. Each ball started with the same speed in random directions.

Prompt for testing: Write a Python script to simulate the motion of three balls (red, green, and blue) inside a static hexagonal arena, where each wall of the hexagon is 200 pixels long. Each ball should have a different size, which corresponds to its weight in the physics simulation. All three balls should start with the same speed but in random directions. The script must handle realistic physics for ball movement, including collision detection with the walls and between the balls, with velocity updates based on their size and weight. Use the Pillow library to render the hexagonal arena and the balls. Save each step of the simulation as an image into a folder, so the frames can later be assembled into a video.

This challenge tested the models' coding, physics, and problem-solving skills, where a structured approach like chain-of-thought prompting—outlining steps before solving—can be especially helpful. By prompting models to focus on key challenges and potential mistakes, even standard models can deliver strong results.

The o1 Advantage

OpenAI’s flagship o1 models are trained to solve complex tasks using detailed internal reasoning, often producing a chain of thought before answering. While powerful, they are slower and more expensive than standard models. For many real-world applications, targeted prompting with faster models offers comparable performance at lower costs.

Model Showdown: Testing Problem-Solving Capabilities

Following are the results of how GPT-4o, GPT-4o-mini, Gemini 2.0, and Gemini 1.5 Flash tackled the Multi-Ball Hexagonal Simulation task. Each model was evaluated for its ability to generate Python code that handled collision detection, momentum conservation, and accurate visual rendering, all within the constraints of a hexagonal arena.

GPT-4o:

OpenAI’s versatile flagship model excels at structured outputs, enabling precise task handling and integration with other software.

  • The code handled the hexagonal arena geometry accurately but displayed balls graphically larger than their physics boundaries, causing visual overlap during collisions.
  • Momentum conservation was incorrectly calculated, with the blue ball moving too much after collisions.
  • Overall, the simulation was functional but lacked physical precision.

GPT-4o-mini:

A smaller, faster version of GPT-4o, ideal for simpler tasks and cost-efficient use.

  • Performed poorly, with faulty arena boundaries and incorrect collision handling for both balls and walls.
  • Generated code lacked the precision required for reliable simulations.

Gemini 2.0 Flash:

Google’s advanced model, designed for complex reasoning and enhanced performance.

  • Delivered the best results, with accurate arena boundaries, correct ball collisions, and precise momentum conservation.
  • The visual rendering and physics calculations were error-free, showcasing the model’s superior capability in this task.

Gemini 1.5 Flash:

A fast and responsive model optimized for efficiency in everyday tasks.

  • While arena geometry was incorrect, the ball collisions and momentum conservation were calculated accurately.
  • The model managed physics better than GPT-4o-mini but was still limited by errors in arena implementation.

Conclusion

The standard models from OpenAI and Google demonstrated strong problem-solving capabilities, with Gemini 2.0 performing the best overall. While the lightweight versions (GPT-4o-mini and Gemini 1.5 Flash) offered faster outputs, their limitations in precision highlight the trade-offs between speed and accuracy in real-world applications.

Structured Outputs – A Key Advantage of GPT-4o Models

One of the standout features of GPT-4o and GPT-4o-mini is their ability to produce structured outputs such as JSON. This capability ensures reliable formatting, making it easier for the models to integrate with software systems or execute multi-step processes accurately. For tasks requiring collaboration with APIs, internet-based queries, or precise control over results, structured outputs allow seamless interaction and precise task execution. This feature is especially critical for complex workflows where consistency and reliability are essential.