An Inter-Dimensional Connection: Fractals and their Traces in Creation

The field of mathematics has proven itself to be one of the most fascinating, yet challenging to grasp, concepts in history. Not only does it provide answers to mindboggling questions, but it can also be found at the heart of our natural world. The specific branch of mathematics we’ll be looking at today are Fractals since they are quite fascinating, and they can be found in both man-made and natural structures, in addition to the fact that they are used in art, technology, and game design.  

Beauty in Complexity  

Let us delve into fractals. In the broadest of terms, fractals are mathematical formulas that create shapes that have self-similarities at different scales, meaning that they infinitely replicate the same shapes at different sizes, and whether you zoom in or out, you’ll find the same overall structure. Though the concept is confusing, it is actually quite simple to observe. Look at clouds in the sky, waves in the ocean, and even lightning strikes, these natural phenomena replicate themselves at different scales and constitute fractals.  

How does this translate into gaming and technology? Well, in today’s gaming market, there are efforts being made to increase efficiency, and many modern titles are relying on procedural generation to accomplish just that. Indeed, it is common for games that rely on replayability such as roguelikes to use procedural generation to create different levels every run. Also, this type of “automatic generation” can also be used for music, especially if the activity that the players are partaking in is meant to take a long time, and this breaks the monotony. Both these feats can be accomplished using fractals as they can help create original music and different terrains that are intricate for the player to explore.  

In fact, many games have already been using fractals for decades now since the results accomplished look quite natural with a high level of variation. From objects to sounds and textures, fractals can be found at the heart of many titles. One of the most famous examples of fractal use is Minecraft, for this game is known for its massive terrains accompanied by caves, lakes, beaches, and even different domains. Also, Spore is a video game that simulates evolution and gives players the ability to create new species, and it has taken the use of fractals to a whole new level by allowing the player to manipulate fractals to create unique lifeforms on each run.  

Procedural Generation  

With the help of modern technology, game developers have access to multiple means of procedural generation, and each one is useful in a specific context. One of the most common methods used is random generation which involves creating assets and items, throwing them in a “bin,” and letting the game decide how it wants to divide them to create different iterations of the same level. Its approach is algorithmic in nature, meaning that there are a set of rules and guidelines used in order to maintain a certain level of consistency. These rules can be defined by the developers, and an example could be to include a weapon shop or specific enemies in a level, no matter its layout. Another method to procedurally generate assets is known as the L-system generation, which is short for “Lindenmayer systems,” named after its creator. This type of generation is specifically used to create complex flora and fauna since it follows a set of rules that can be manually made complex or simplistic. No Man’s Sky, a space exploration game, relies on this method to create its rich environment that the player mines through.  

The difference between the different types of generations lies in order and chaos. In other words, depending on the level of consistency and order that the developers wish to achieve, they must pick the appropriate method of generation. Fractals, for instance, allow for a high level of order and intricate designs since they follow mathematical formulas that can clearly be defined. On the other hand, random generation, as the name suggests, is more unpredictable and can be used for chaotic level design that follows a central theme but is completely different every time. There are no clear winners, and each method is useful in different contexts. It is even common for developers to utilize different generation techniques in the same game.  

Conclusion 

All in all, fractals are quite fascinating, and they have proven useful in a variety of fields, but especially in game design. This complex concept allows for the generation and simulation of natural terrains in a virtual landscape, and it allows designers to bring the beauty of the real world as well as its intricacies into the world of a game without seeming forced or out of place. Also, the idea of endless repetition of the same calculated structures at different scales is fascinating in its own regard, and it truly shines a light on the astounding nature of the world we live in.