Tixy.land showcases a 16x16 pixel animation created using straightforward mathematical formulas. Each frame is generated by applying simple rules, specifically binary operations and modulo arithmetic, to the x and y coordinates of each pixel. The result is a mesmerizing and complex display of shifting patterns, evolving over time despite the simplicity of the underlying math. The website allows interaction, letting users modify the formulas to explore the vast range of animations achievable with this minimal setup.
The webpage "tixy.land" presents a captivating demonstration of how complex and visually appealing animations can be generated from remarkably simple mathematical principles applied to a 16x16 grid of dots. Each dot on this grid, conceptually arranged like pixels on a tiny screen, is individually manipulated over time based on its coordinate position (x, y) and the current frame number (t). The brilliance of the system lies in the concise formulas that dictate each dot's state – either on (bright) or off (dark). These formulas, leveraging trigonometric functions like sine and cosine along with basic arithmetic operations, create intricate patterns of light and dark that evolve dynamically as the frame count advances.
The resulting animation exhibits a mesmerizing interplay of oscillating waves, radiating bursts, and intricate geometric formations, all emergent properties of the underlying mathematical relationships. The seemingly simple rules give rise to a surprisingly rich and varied visual experience. Although the display is constrained to a small 16x16 grid, the clever use of mathematical functions allows for a remarkable degree of complexity and artistry to emerge from the limited resolution. The webpage itself serves as a testament to the power of algorithmic art, showcasing how aesthetically pleasing and dynamically evolving visuals can be produced from a minimal set of instructions and a confined digital canvas. The user is presented not only with the captivating animation but also with the underlying mathematical formula, allowing for an appreciation of the elegant connection between the code and the resulting visual output. Furthermore, the site allows for interactive exploration, inviting users to modify the formula and observe the resulting changes in real-time, thereby fostering a deeper understanding of the relationship between mathematical expressions and visual art.
Summary of Comments ( 41 )
https://news.ycombinator.com/item?id=43942881
Hacker News users generally praised the simplicity and elegance of Tixy.land. Several noted its accessibility for understanding complex mathematical concepts, particularly for visual learners. Commenters discussed the clever use of bitwise operations and the efficiency of the code, with some analyzing how specific patterns emerged from the mathematical rules. Others explored potential extensions, such as adding color, increasing resolution, or using different mathematical functions, highlighting the project's potential for creative exploration. A few commenters shared similar projects or tools, suggesting a broader interest in generative art and simple, math-based animations.
The Hacker News post "A simple 16x16 dot animation from simple math rules" (linking to tixy.land) generated a moderate number of comments, mostly expressing fascination with the visual effect and exploring the underlying mathematics.
Several commenters expressed sheer enjoyment of the visual patterns created by the simple rules. Phrases like "mesmerizing," "hypnotic," and "beautiful" were common. Some appreciated the elegance of achieving complex visuals from minimal code and math.
A few commenters delved into the mathematical principles at play, discussing concepts like bitwise operations, modular arithmetic, and the nature of cyclic patterns. One commenter pointed out the connection to cellular automata, specifically mentioning Wolfram's Rule 30, known for producing complex patterns from simple rules. Another explained how the code essentially generates a sequence of numbers and then uses bitwise operations to translate each number into a visual pattern on the 16x16 grid. This explanation helped clarify how such minimal code could produce such dynamic visuals.
Some commenters explored variations and extensions of the concept. One suggested modifying the parameters to see how the patterns change, while another proposed implementing the animation in different programming languages or platforms like Shadertoy. There was also discussion about the efficiency of the JavaScript implementation, with some commenters suggesting optimizations.
A few commenters linked to similar projects or mathematical concepts. One linked to a project visualizing Conway's Game of Life, highlighting the similar theme of simple rules generating complex behavior. Another linked to a resource on cyclic group theory, suggesting it as relevant background information for understanding the mathematical principles involved.
While many appreciated the visual and mathematical aspects, some comments expressed a desire for more interactivity or control over the animation. They suggested adding features like the ability to pause, step through the animation, or modify the parameters in real time.
Overall, the comments reflect a strong appreciation for the elegance and surprising complexity of the animation. The discussion explored the underlying mathematics, suggested extensions and variations, and connected the project to related concepts in computer science and mathematics. While some desired more interactive features, the general sentiment was one of fascination and curiosity.