The concept of fractals in the Quran can be explored through the lens of recurring patterns in nature, self-similarity, and divine order. While the Quran does not explicitly mention "fractals" (a term coined in modern mathematics), it frequently describes natural patterns that align with fractal geometry, reinforcing the idea of a unified and recursive design in creation.

Key Themes of Fractal-Like Concepts in the Quran

1. Repetition and Self-Similarity in Creation

The Quran repeatedly emphasizes the idea that patterns found in the macrocosm (the universe) are reflected in the microcosm (human beings, nature). This aligns with the fractal property of self-similarity, where the same structure appears at different scales.

"We will show them Our signs in the horizons and within themselves until it becomes clear to them that it is the truth." (Quran 41:53)

This verse suggests that divine signs manifest both in the vastness of the cosmos and within human beings, hinting at a recurring pattern across different scales of existence.

2. Patterns in Nature Reflecting Divine Order

Many Quranic verses describe natural phenomena that exhibit fractal-like structures, such as mountains, clouds, trees, and the branching of rivers.

"Do you not see how Allah has sent down water from the sky and caused it to penetrate the earth as springs? Then He brings forth thereby crops of varying colors, then they dry and you see them turning yellow; then He makes them scattered debris. Indeed, in that is a reminder for those of understanding." (Quran 39:21)

The process of rainfall, vegetation growth, and decay follows iterative and recursive patterns seen in nature, reflecting fractal geometry.

3. The Tree as a Symbol of Growth and Repetition

The Quran often uses the metaphor of a tree to describe both spiritual and natural growth. A tree's structure—branches growing from a trunk, mirroring smaller branches at different levels—is a fundamental example of a fractal.

"Do you not see how Allah presents an example? A good word is like a good tree, whose root is firmly fixed and its branches are high in the sky." (Quran 14:24)

This verse can be interpreted as describing both a literal tree and a fractal-like spiritual truth, where a small action (like a word) can grow into something vast and interconnected.

4. The Cycle of Creation and Recreation

The Quran speaks of cycles in creation, destruction, and recreation, much like the iterative nature of fractals.

"And it is He who begins creation; then He repeats it, and that is [even] easier for Him." (Quran 30:27)

This cyclical process resembles the fractal property of infinite recursion—where patterns repeat across different scales and dimensions.

Conclusion

The Quran’s descriptions of nature, cosmic order, and spiritual concepts resonate with the principles of fractal geometry. While the term "fractal" is modern, the Quran’s emphasis on self-similarity, repetition, and infinite complexity in creation suggests a deep alignment with fractal patterns observed in the universe. This perspective highlights the Quran’s timeless wisdom in describing the intricate designs embedded in the fabric of existence.