A simulator that aims to simulate a world based on Dark's concept of time travel. It is not mandatory for you to have watched Dark. Understanding of the below mentioned concepts is sufficient.
For the sake of simplicity, let us consider a finite two-dimensional space where the time and space are quantised. That is, the world is a two-dimensional grid, where beings can move only along the grid. Let us also consider that an being is of the size of a grid (a being cannot span over two grids). For each step in time, a being can either stay in place, or move in one of the available directions. Also, two beings cannot overlap.
Each being in the grid can move to one of the shown possible positions in the next time step
Each being gets a set of inputs and performs actions based on those inputs. Generally the input would be some representation of the entire state of the world. For example, the input could be a 100 element array of numbers, one element for each grid where 0 is for empty, 1 for green, 2 for blue etc.
The 4 x 100 matrix is the brain of the being.
If the above doesn't make sense to you, just think that their behaviour doesn't change with time and can be predicted accurately if positions of every being is known.
Each being has a fixed life time after which it will cease to exist.
There is a specific location in the world if reached by beings, enables them to travel through time.
A black hole at the end of the world.
Whenever a being lands on the black hole, it has two more choices. It can travel to the past by 10 steps (variable) or to the future by 10 steps. Again, all these decisions can be exactly predicted given the decision mechanism. We also prohibit travel beyond the origin to negative time.
Whenever someone travels to the future for 10 frames, the being dissapears on the next time step and reappears after 10 time steps with the same age.
Whenever someone travels to the past for 10 frames, their presence is mandatory in the (n - 10)th frame. That is, in the (n - 10)th frame, there are two beings who are the same, but one, 10 frames older than the other. The future causes the present.
In order to avoid ambiguities regarding the physical destination, after travel, the being ends up at the top left corner of the world. If the position is occupied, they are placed one block to the right and so on.
Our aim is to simulate this 10x10 world for a given initial configuration for a given amount of time steps. The concept of time travel introduces a lot of degrees of freedom. There are a lot of solutions for a given initial configuration. We should be abled to simulate at least one of them if not all. Remember, the brains of the beings are unaltered at any given time and each decision can be accutarely predicted given the current state of the world.
Please feel free to post issues for suggestions / for a better understanding of the concept.
The proposed method is to construct a tree of possible next moves considering the possibility of time travel in the future. That is, for each frame, we also consider that someone, 10 frames to the future, travels to the past. To resolve this, we first move beings according to their will as normal. We then place 3 more parallel frames (3 in this case because we have 3 individuals) on the same step where each frame has an additional one of the three beings on the top left. This additional being is 10 frames older than the respective normal-time being. This is to account for any possible time travels in the future.
A state branching to possible states in the next time step.
Note: All the numbers in the above examples are variables and can be anything for a given world. 10 frames could instead be 33 frames 😉
See #2.
The approach was to stay on the main track till a being lands on the black hole. Alter history if and only if travelled.
There are two places where this approach would fail.
There are a few valid cases which will not be considered if we branch only when we hit the black hole. For example, consider this situation.
- There is a single being in the whole world.
- His brain is such that when he's alone, he would never reach the black hole.
- If someone else is present with him, he might reach the black hole.
In this case, there could be a path where a being from the future influences the being in present time to get into the hole. Note that the being entering the hole in the first place is caused by the travelled being. If we branch only when someone hits the portal, we will miss this path. See predestination paradox.
Important: If a being is alone in the world in a particular time step, he never travels through time in the next step.
Another reason this approach would fail is that once someone hits the portal, history has to be rewritten. If rewritten, there is a chance that the being never hits the portal in the first place. So you'll have to update this by dropping a branch. This will happen back and forth resulting in an endless loop.