# The Meta-Metaverse: Ideation and Future Directions
## 3 Fractals and the Meta-Metaverse  
Fractals are complex and repetitive designs that appear in many natural occurrences, like mountain ranges and snowflakes, as well as in computer-generated and mathematical designs [33; 34; 35]. They possess self-similarity, meaning that the design repeats itself at varying scales. Fractals are adept at representing complexity and detail compactly, and their most defining trait is their infinite level of intricacy [36]. As you zoom in on a fractal pattern, you will find smaller and smaller copies of the overall design, and the pattern repeats indefinitely [37]. This occurs because fractals are produced using a set of equations or rules that generate a geometric form that repeats itself on different scales. Aside from their application in describing natural phenomena, fractals are employed in various fields, such as engineering, computer graphics, and physics. Different types of fractals exist, each with its own distinct set of rules and properties, such as the Mandelbrot set, Julia set, and L-systems [38; 39; 40]. These varied fractals offer vast potential applications, and they have been utilized to model a wide range of phenomena, from the growth of plants to the movement of stocks in the stock market. Fractals are mathematical patterns that display self-similarity, indicating that the same pattern repeats at different scales [41; 42]. This feature provides fractals with their characteristic \"fractal\" appearance, which seems \"rough\" or \"broken\" due to the irregularity of the pattern. Fractals can be found in various natural and artificial systems and are used in many fields for diverse purposes. In physics, fractals model numerous phenomena, including the mass distribution in the universe, plant growth, and fluid flow. Computer science employs fractals to create computer graphics and design algorithms for solving complex problems [43; 44]. Engineering utilizes fractals in designing antennas and other structures that work effectively across a broad range of frequencies. Fractals are also used in the medical field to study the structure and function of biological systems [45], such as the vascular system and the lungs [46], and in psychology to investigate perception and cognition and their role in visual information processing [47]. In summary, fractals are a valuable tool for comprehending and modeling complex systems in diverse fields, with significant applications in science and technology. Fractal principles have been employed in the creation of computer networks and communication systems in order to enhance the speed and effectiveness of data transmission [36]. By making use of the self-repeating patterns that exist within the data being transmitted between nodes, these systems can be designed to transmit data more efficiently. Fractals are utilized in order to optimize the design of these systems, leveraging the self-similar patterns to improve the speed and efficiency of data transmission. The application of fractal concepts to the design of computer networks and communication systems has thus led to significant improvements in the transmission of data between nodes. The concept of utilizing fractal patterns as an infrastructure idea to connect several metaverse platforms and digital twins within each other offers a unique approach to accessing and exploring digital representations of everything in the world, ranging from materials to phenomena. This idea involves organizing the infrastructure in a fractal-like structure, where each layer contains its own digital version. At the core of this concept lies the self-similarity and infinite intricacy of fractals. By adopting a fractal-based structure, the infrastructure can accommodate multiple layers, each representing a different level of detail or abstraction. Just as a fractal repeats its pattern at varying scales, this infrastructure enables the integration of various metaverse platforms and digital twins, connecting them within the overarching framework.