July 24, 2024

Paul Pham

12th Grade

Fountain Valley High School

Minecraft Worlds

Minecraft, as many are familiar, contains expansive worlds through which players can freely explore and build upon their imagination. In a certain sense, as Minecraft and Mojang developer Henrik Kniberg puts it, Minecraft is an Earth simulator, with various creatures, mountains, trees, flora, daylight cycles, and climates across a seemingly endless world of blocks. These seemingly endless worlds are unique in landscape, terrain, and size. When you load into a new Minecraft world, it is almost certainly a world nobody has ever seen. 

Distinguishing these worlds from one another comes from their world seeds, with each world being assigned a unique world seed of several numerical values ranging from -9,223,372,036,854,775,808 to +9,223,372,036,854,775,807 that determine how the blocky world generates. With this, there are then therefore 18,446,744,073,709,551,616, or 18 quintillion, or 264, different world seeds, meaning there are 18 quintillion worlds in Minecraft all vastly different in nature and terrain. Furthermore, each of these 18 quintillion worlds contains a total area of 3.6 billion km2, with each individual block being 1 m2. This value puts each world approximately seven times the size of Earth which is 0.5 billion km2. 18 quintillion worlds, then, with a size of 3.6 billion km2 exist in Minecraft. How quite extraordinary.

These incomprehensible numerical values that outline the expansive catalog of equally expansive and unique Minecraft worlds raise the question of how this came to be. How has Minecraft created 18 quintillion worlds with each world having 3.6 billion km2 of diverse landscape and each world being vastly different in nature from one another? Well, this great feat has been achieved through a method called procedural terrain generation, a highly efficient means of creating digital worlds.

Procedural terrain generation occurs in various steps. 

The first and foremost step is terrain shaping, a process that determines which blocks in a chunk are solid and which others are not, initially placing either a stone block or an air block in each appropriate location. 

It is then determined which area of the chunk is in an ocean or sea level placement, and thereafter water is placed in these determined spots.

From there, the surface of the solid stone land is replaced according to the appropriate biome, where forest biomes have grassy surfaces, desert biomes have sandy surfaces, etc.

Finally, the surface is decorated with details such as trees, long grass, villages, and structures while the underground is decorated with ores, cave systems, dungeons, and other structures.

Perlin Noise is one method to achieve a state of what is called Gradient Noise. Perlin Noise is the method that takes a wide array of arbitrary pixels or entities and makes each pixel or entity blend similarly with the pixel or entity beside it, resulting in a smooth, gradient-like texture.

Imagine, then, that the gradient textured image is a topographical map showing the x and z axis of a world, with the black, darker spots representing dips and valleys and the white, lighter spots representing peaks and mountains. The world, then, contains a natural and smooth pattern of mountains and valleys. Perlin Noise can be calculated through third-party sources, meaning that a developer need not calculate it themselves, making it a convenient means of generating terrain. Applying the Perlin Noise to the procedural terrain generation function, we get a smooth world.

Still, there remains a degree of bleakness, so to further variate this, a trick called octaves can be used. 

However, despite its natural smoothness and randomness, it lacks geographical abnormalities, abnormalities that make real-life Earth beautiful and unique, resulting in a rather uneventful landscape repetitive in its nature of fluctuation. Among some of these geographical abnormalities can be harrowing cliffs, towering mountain ridges, regal river valleys, and quiet plateaus where nature grows freely. How can we implement these geographical abnormalities while maintaining realistic degrees of randomness and smoothness? This is achieved through noise transformation and the use of spline points on a spline curve. 

Spline curves are graphs that contain selected points called spine points, and a line or curve is drawn to fit most appropriately to the sequence of spline points. An example is provided here: 

Values called continentalness ranging from -1 to +1 can be assigned to each block in a Minecraft world with relatively minor increases from one block to the next one beside it. For example, one block can have a continentalness of 0.016, the block next to it can have continentalness of 0.022, then the next 0.028 or the next 0.014, etc. Creating a splint curve thereafter by putting continentalness on the x-axis and terrain height on the y-axis and selecting various values of continental ness and assigning with a certain terrain height, the separate points assigned to each value can be connected to create an irregular graph as such:

Further variation is done beyond respecting just the parameter of continentalness, such as with respect to the parameters of erosion and peaks & valleys. Each parameter has its own configuration of amplitudes and octaves. Each block in a world not only has an assigned value of continentalness, but also of erosion and peaks & valleys. 

These parameters are then taken into consideration and given a spline curve that further variates the terrain of the world.

This combination of variations produces an amazing world generation whose terrain is dramatic and unpredictable, as such:

Squash factor and height offset are the two parameters that control this terrain generation. Flat terrain is most prominent with a high squashing factor while a low squashing factor produces wild, unorganized, and unpredictable terrain. Height offset shifts the base terrain elevation either up or down. These are determined with the previously mentioned spline curves and the three noise transformation parameters.

Cave systems are generated using the same approach of assigning individual blocks gradual density values and utilizing noise in noise fields. On a noise graph, darker blocks can be identified as either solid or air blocks, with the lighter blocks being the other option. With this, there is a gradual pattern of solid-to-air blocks deep underground to generate gradual caverns. Minecraft developer Henrik Kniberg terms these caves “cheese caves” for their apparent cheese texture.

These individual yet carefully interlaced factors, terrain shaping, mathematics and trigonometry, coding, spline graphing, and Perlin Noise among some of them, synthesize together to generate awesome, dramatic, unpredictable, and unique worlds within the game of Minecraft on a simply grand scale. The wild generation of terrain is one of the iconic qualities of Minecraft’s imaginative nature and provides endless canvasses for a player’s creativity. 18 quintillion of these well-crafted worlds exist for players all around the world to load in and decorate with builds and memories. 

In my youth, I thought that Minecraft developers spent ages placing blocks individually to build each Minecraft world, and that amazed me. Yet procedural terrain generation, though much more convenient and efficient, amazes me much more with its digital and mathematical intricacies, yielding a much more sophisticated approach to world generation. I hope that perhaps you too have been fascinated by such methods, and to henceforth explore and adventure through Minecraft’s expansive worlds. 

I shall leave off with some wonderful scenes I have captured of Minecraft terrain generation.