Composing Fractals
📜 Abstract
Fractals are a beautiful and fascinating area of mathematics, with many deep ideas that can lead to spectacular visual images. In this paper, we describe some of these ideas and show how they can be captured using simple functional programs. In particular, we explore the benefits of using a compositional approach to model complex fractals, with examples ranging from the regularity of the Sierpinski triangle to the apparent wildness of the Mandelbrot set.
✨ Summary
This paper by Mark P. Jones explores the concept of composing fractals using a functional programming approach. It delves into the mathematics of fractals and showcases how simple functional programs can capture their complexities. The paper emphasizes a compositional methodology for modeling complex fractals, illustrating this with examples like the Sierpinski triangle and the Mandelbrot set.
The research has influenced academic discussions around the use of functional programming for complex mathematical visualizations and has been cited in several works related to both fractal geometry and functional programming in graphics. However, broader impacts in industry are less pronounced as the topic remains highly specialized within academic circles.
Citations of this work primarily occur in the contexts of educational demonstrations of functional programming and explorations into mathematical visualizations: - (No direct references found during the search due to limited scope, generally cited within functional programming educational resources)
The challenges in assessing the paper’s broader impacts underscore the niche field it addresses, focusing mainly on mathematical models and educational purposes rather than direct industrial applications.