The Frontier is a region of space trapped within the chaotic gravitational forces of three ever-shifting black holes: the Trinary. Comprised of several regions, our simulation is further separated into constellations made up of solar systems. You will travel between these disparate systems, searching for territory to control and topology to tame, adapting to the environmental conditions of each location to survive. However, this will not come freely: the harsh nature of space guarantees that everything will erode over time. Your fight against entropy and upkeep will require vigilance to remain in control.   

By grounding the experience in scientific principles, we want to create as real a galaxy as possible, allowing you to rely on your intuition and understanding as you navigate the Frontier.

Simulating such a galaxy is no small undertaking. This is how the Frontier, which hosts the mighty Trinary, has come to unfold so far.

To simulate the Frontier, we must first define its initial conditions: its structure, the number and properties of black holes (and the distance between them), the distribution of solar systems, and the initial velocity. 

Galaxies are gargantuan. Though they vary in size (with the tiniest dwarf galaxies containing stars numbering in the thousands), galaxies comparable to our Milky Way house hundreds of billions of stars. Galaxies come in different shapes, from beautiful spiral galaxies to irregular galaxies with seemingly little structure. A typical spiral galaxy has three fundamental building blocks. Most notable is the disc. These pizza-like arrangements encompass most of the galaxy's stars. Second is the galactic bulge, a dense grouping of stars at the galaxy's center. The third building block is the theoretical dark matter halo, a cloud of invisible matter surrounding the galaxy that makes up the bulk of the galaxy's mass and has great gravitational pull. The properties of dark matter are still unexplained, even though we have observed its gravitational effect on galaxies – i.e. why the velocities of stars farther from the galaxy's center are so high.

BG3_LR

galaxy

Supermassive black holes are found at the very center of most galaxies. Though they are enormous and emit profound gravitational influence, supermassive black holes are perhaps not as massive compared to their parent galaxies as one might think. For example, the Milky Way‘s central black hole, Sagittarius A*, has a mass of 4.3 million suns, only around 0.0004% of the galaxy's mass. For reasons unknown, Frontier’s galaxy has been malformed by the presence of the Trinary - three supermassive black holes bound in an endless dance. The gravitational force of the Trinary has a radical impact on how the entire galaxy is formed, as each celestial body is affected by their immense magnitude.

stars

Beyond mass, stars have many other attributes that distinguish them, for example: size, temperature, age, and metallicity. We classify main-sequence stars (stars that haven't evolved into red giants, gone supernova, etc.) into seven different classes. From the smallest to most enormous are M-type stars, K-type, G, F, A, B, and O-type stars. As an example, our sun is a G-type star. 

A part of the simulation is to create a natural distribution of different types of stars and planets within varied solar systems clustered together that then form the wider Frontier galaxy. Each of these solar systems contain different elements (moons, asteroid fields, etc.) which vary: where the solar system is located in the galaxy, its proximity to other phenomena (for example, close to a supernova or a pulsar), and the amount of stars that are in each solar system. This way, when the inhabitants of the Frontier travel the galaxy , they will truly experience a unique environment.

Turning particles into a galaxy using astrophysics

Considering these galactic components, a simulation of their forces and how they interact is needed.

In the 17th century, Sir Isaac Newton developed calculus to explain the natural phenomenon of gravity.  

calculus

His famous equation explains the motion of everything, from an apple falling from a tree to the motion of heavenly bodies. It helps explain the orbits of moons and planets and the movements of stars and entire galaxies. 

The law of universal gravitation lies at the heart of EVE Frontier‘s galaxy: to create it, we have been working on simulating the motion of countless particles under the influence of gravity via the n-body simulation. These particles can then be used as points of reference for the matter within Frontier (currently solar systems and clusters of solar systems). As said, we want EVE Frontier to feel as natural as possible by grounding its galaxy to the laws of physics and the Digital Physics which underpin its existence. 

You may have heard of the three-body problem, which aims to predict the trajectories of three-point masses. Although the two-body problem was solved hundreds of years ago, additional bodies make the system too chaotic and unpredictable. We are working on a simulation that solves this problem as closely as possible. 

The simplest way to carry out an n-body simulation is with a direct sum algorithm. This means calculating the gravitational forces acting on any given body by each of the other n-1 particles and adding them together. Using a direct sum algorithm, we could calculate the total force acting on all bodies and, thus, how far the particles move in one timestep. We could then move to the next timestep and repeat the procedure. This algorithm is simple and effective but has one glaring downside: having order O(n^2), making the simulation of the galaxy very inefficient as we introduce more particles.

Doubling the number of particles in the system would quadruple the time for a complete simulation. To perform 10,000 or even 100,000-body simulations, we need a different algorithm. 

Due to the complexity of the direct sum algorithm (O(n^2)), and the aim for the galaxy of EVE Frontier to be simulated in detail, we have instead been using the Barnes-Hut simulation, the scientific standard for these types of astrophysics computations. With its O(n*log(n)) complexity, the Barnes-Hut simulation is substantially faster than the direct sum algorithm, especially as it grows in size and complexity. 

To calculate the force of one particle, you can group particles to make the calculation easier – which is why our current simulation is divided into an octree structure, whereby the volume is sliced into eight equally sized cubes. When calculating the gravitational force for a given particle, we only need to use the direct summation approach for neighboring bodies that lie relatively close to our particle. Particles that are sufficiently far away can be treated as a single object with their combined mass centered at their cube's center of mass. In short, this Barnes-Hut octree algorithm is how we execute n-body simulations. 

The box in this video is a 2D representation of this. To calculate the force of one of these particles, you don't need to sum the forces of each of the other particles directly – but rather sum the masses of each box and calculate the force from the center of mass of each box. This makes the calculation much shorter. If we were using a direct sum algorithm, you would have to calculate all n forces acting in it, one for each particle. However, by splitting it into a specific number of boxes, you only need to calculate the force from each box that is not empty, thus making the calculation more efficient.

We now have the initial conditions defined, combined with a way to simulate the forces at play and the ambition to simulate a range of cosmological scenery within the Frontier itself. We have created thousands upon thousands of particles and assign their initial positions and velocities based on statistical distributions of different galaxy building blocks. We also use functions like the Initial Mass Function to help translate the particles in the simulation to a more detailed and accurately representative galaxy layout.

In our latest version, these particles represent clusters of solar systems. We then created a more significant body at the center of each of these as a centerpiece and used the Barnes-Hut algorithm to evolve the body’s positions over time.

Watch our current simulation in motion: in the video, the colors are derived from a colormap, which accounts for acceleration, i.e., the faster something is accelerating, the more force it experiences and the redder it gets:

This is how the galaxy of EVE Frontier will collide into existence, creating a wildly disparate and chaotic series of environments for you to explore and expand your influence in an uncharted and hostile part of space.

Into the Frontier

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