[Paper Review] Quasi-random Agents for Image Transition and Animation

Aneta Neumann, Frank Neumann+1 more|arXiv (Cornell University)|Oct 20, 2017

Mathematical Dynamics and Fractals18 references3 citations

TL;DR

This paper introduces a novel method for image transition and animation using multiple agents performing quasi-random walks on a grid, where each agent follows a deterministic sequence of directions to paint a target image. By allowing artists to define custom rotor sequences, the approach enables controllable, reproducible, and artistically diverse animations with minimal randomness, achieving varied visual behaviors through feature-based analysis of artistic properties like colorfulness and contrast.

ABSTRACT

Quasi-random walks show similar features as standard random walks, but with much less randomness. We utilize this established model from discrete mathematics and show how agents carrying out quasi-random walks can be used for image transition and animation. The key idea is to generalize the notion of quasi-random walks and let a set of autonomous agents perform quasi-random walks painting an image. Each agent has one particular target image that they paint when following a sequence of directions for their quasi-random walk. The sequence can easily be chosen by an artist and allows them to produce a wide range of different transition patterns and animations.

Motivation & Objective

• To develop a controllable alternative to random walk-based image animation that reduces unpredictability.
• To generalize quasi-random walks (rotor-router models) to multiple autonomous agents for image painting and transition.
• To enable artists to define custom direction sequences to influence the visual behavior of animations.
• To analyze the resulting animations using artistic features such as colorfulness, contrast, and hue for qualitative and quantitative evaluation.
• To demonstrate that quasi-random walks produce diverse, artistically interesting animations with predictable, tunable behaviors.

Proposed method

• Each agent performs a quasi-random walk on a 2D grid using a fixed, deterministic sequence of directions (e.g., right, down, left, up).
• At each visited pixel, the agent paints the corresponding pixel from its target image and updates the rotor (direction pointer) to the next in its sequence.
• The rotor at each grid cell cycles through a predefined permutation of the four cardinal directions, ensuring deterministic traversal.
• Multiple agents operate in parallel, each painting a different image or the same image, creating transitions or animations.
• The user-defined rotor sequence governs the agent’s path and visual output, enabling artistic control over motion patterns and image blending.
• A feature-based analysis evaluates animations using metrics like Benford’s law, Global Contrast Factor, Colorfulness, and Mean Hue to assess artistic behavior.

Experimental results

Research questions

• RQ1 How can quasi-random walks be generalized to enable controllable image transition and animation using multiple agents?
• RQ2 What artistic behaviors emerge from different rotor sequences in multi-agent quasi-random walks?
• RQ3 How do different rotor sequences affect visual features such as contrast, colorfulness, and hue during animation?
• RQ4 To what extent do quasi-random walks replicate or differ from expected random walk behaviors in artistic image generation?
• RQ5 Can user-defined rotor sequences produce predictable, artistically diverse, and visually compelling animations?

Key findings

• Animations using 4 agents with long, asymmetric rotor sequences produced the highest Benford’s law values, indicating less natural, more chaotic behavior.
• The Global Contrast Factor was highest for animations using repetitive sequences with 2 or 4 agents, indicating richer contrast and stronger visual attention.
• All animations stabilized around a Colorfulness value of 140–145 after 1,000,000 steps, except for 4-agent symmetric sequences, which showed regular temporal variations.
• Mean Hue values for 4-agent symmetric sequences exhibited alternating high and low values after ~2.5 million steps, indicating chaotic motion patterns.
• Animations with 2 agents using long, asymmetric sequences showed the most stable and regular behavior across all features, suggesting predictable, natural-looking motion.
• The 4-agent symmetric sequence animation displayed the largest variation in Mean Hue, confirming its chaotic and dynamic visual character.