Geometry of Complexity in Mathematics and Computing Fractals
Session
Computer Science and Communication Engineering
Description
Fractals are structures that reveal infinitely complex patterns yet are surprisingly simple. They emerge as objects defined by recursion and they capture the idea of selfsimilarity. Beyond visual appeal, fractals also carry deep mathematical significance, bridging geometry, analysis and chaos theory. They challenge the very concept of dimension, expanding the understanding of geometry that exists beyond the Euclidean limits. In computer science, algorithms for generating these fractals rely on recursion, iteration and complex numbers. As coding provides a base for fractals to show how mathematical beauty can be showcased in the digital world, in generating landscapes, textures, organic forms and realism. These however not being the only functions but also supports data compression, image recognition, and modeling of chaotic systems. They stand as a powerful intersection between abstract theory and applied computation, embodying the synergy of math and computer science. Their paradoxical nature is part of their allure. On one hand, they are born from equations that can be written in a few lines. On the other, they give rise to visuals so complex and alive that they seem beyond calculation. In this sense, fractals appear less like human inventions and more like discoveries of a hidden order already woven into nature itself. Fractals remain both familiar and alien glimpses of infinity that we can generate but never fully grasp. As we look closer, we find they are not only art and not only mathematics, but a bridge between the two, pointing toward patterns that seem to echo across science, technology, and even philosophy.
Keywords:
Fractals, Chaos, Mathematics, Functions, Computer, etc
Proceedings Editor
Edmond Hajrizi
ISBN
978-9951-982-41-2
Location
UBT Lipjan, Kosovo
Start Date
25-10-2025 9:00 AM
End Date
26-10-2025 6:00 PM
DOI
10.33107/ubt-ic.2025.86
Recommended Citation
Taraku, Diell and Leka, Hizer, "Geometry of Complexity in Mathematics and Computing Fractals" (2025). UBT International Conference. 18.
https://knowledgecenter.ubt-uni.net/conference/2025UBTIC/CS/18
Geometry of Complexity in Mathematics and Computing Fractals
UBT Lipjan, Kosovo
Fractals are structures that reveal infinitely complex patterns yet are surprisingly simple. They emerge as objects defined by recursion and they capture the idea of selfsimilarity. Beyond visual appeal, fractals also carry deep mathematical significance, bridging geometry, analysis and chaos theory. They challenge the very concept of dimension, expanding the understanding of geometry that exists beyond the Euclidean limits. In computer science, algorithms for generating these fractals rely on recursion, iteration and complex numbers. As coding provides a base for fractals to show how mathematical beauty can be showcased in the digital world, in generating landscapes, textures, organic forms and realism. These however not being the only functions but also supports data compression, image recognition, and modeling of chaotic systems. They stand as a powerful intersection between abstract theory and applied computation, embodying the synergy of math and computer science. Their paradoxical nature is part of their allure. On one hand, they are born from equations that can be written in a few lines. On the other, they give rise to visuals so complex and alive that they seem beyond calculation. In this sense, fractals appear less like human inventions and more like discoveries of a hidden order already woven into nature itself. Fractals remain both familiar and alien glimpses of infinity that we can generate but never fully grasp. As we look closer, we find they are not only art and not only mathematics, but a bridge between the two, pointing toward patterns that seem to echo across science, technology, and even philosophy.