Rotor-router symetries with an absorbing pixel

Discovering Symmetry in the Rotor-Router Algorithm: A Fascinating Observation!

Are chips being generated from the left or the right?

The answer may surprise you.

The rotor-router model has the ability to simulate complex patterns and behaviors that may be observed in the physical world. In this page, we will explore the symmetrical patterns that can be generated using an absorbing pixel in the rotor-router model.

An absorbing pixel is a space unit that absorbs any chips that pass through it, rather than reflecting or transmitting them like a reflective or transparent pixel would. By introducing an absorbing pixel into the rotor-router model, we can observe the symmetrical patterns that emerge as the chips move through the space.

One interesting aspect of this experiment is the way in which the absorbing pixel can act as a sink for the chips, drawing them in and creating a vortex-like pattern around it. This behavior is similar to the way in which a black hole in the physical world can act as a sink for matter, drawing it in and creating a gravitational field around it.

Overall, the rotor-router model with an absorbing pixel offers a unique perspective on the symmetrical patterns and behaviors that can emerge in a given space. It provides a promising avenue for further exploration and research into the fundamental principles of the universe and its behavior.

In this experiment, we explored the behavior of the rotor-router algorithm in a closed environment with reflective walls and an absorbing pixel. We discovered that the absorbing pixel creates a symmetry in the pattern formed by the rotor-router algorithm, with the moiré pattern around the emitting point being similar to the moiré pattern around the absorbing point. This symmetry suggests that the process of inserting or extracting a chip from the system has a similar effect on the diffusion pattern on the background. These findings add to the intriguing nature of the rotor-router algorithm and its potential for further exploration and study.

When adding an absorbing pixel which eats the chips of the rotor-router in a closed environnement with reflective walls, we discover some symetries. Hier e above the ULDR (up left down right) version of the rotor router. We see the symmetry is partially broken compared to the UDLR posted before. The pattern at emitting point is still there (almost identical) at the absorbing point.

An absorbing point put the background space in the same configuration as an emitting point. Funny discovery there!

The second snapshot above shows early steps of the algorithm.

This property of the rotor-router algorithm is exciting. The rotor-router when launched from a given center give raise of a kind of moiré around its center.

The amazing property I found here is that if we add an absorbing pixel in the map, the same moiré pattern builds itself around that absorbing point. We may infer here a sort of symetry of the process : inserting or extracting a chip give the same diffusion pattern on the background.

While running for the first time the rotor-router algorithm with an absorbing pixel in the closed environment with reflective walls, I was struck by the symmetry of the patterns that emerged. As the algorithm progressed, I noticed that the pattern on the absorbing pixel was starting to resemble the pattern at the emitting point. At first, I couldn't believe my eyes - it seemed impossible that such a symmetry could exist. But as I continued to run the algorithm and observe the patterns, the symmetry became more and more clear. I was astonished to see this for the first time, and it sparked my curiosity to explore the potential applications and implications of this symmetry in more depth.

Here below my first exploration of the rotor-router algorithm, I was amazed to see the formation of a pattern on the absorbing pixel.

Here below a second experiment showing how symetrical is the rotor-router algorithm when we add an absorbing pixel.

In this picture I setup the UDLR rotor router center on the left and I add a single absorbing pixel on the right. I put reflective walls (in blue) for the rotor chips. You may notice how similar the patterns on the emitting and absorbing side are. You may also see how field lines are bended and attracting each other.

Here below is the same test with UDLR rotor router center on the left

, the absorbing pixel on the right and a single 10x10 slit in the center.

The diffusion pattern occurs on the slit.

In this specific experiment, we see that the rotor-router algorithm generates a diffusion pattern on the single slit in the middle. This is an interesting observation, as it suggests that the rotor-router model may be able to capture some of the quantum phenomena observed in experiments like the Young double-slit experiment. It is especially intriguing to see that the particles in this model can pass through the slit multiple times, potentially indicating the existence of a background for momentum interactions in this alternate theory. Overall, this experiment highlights the potential of the rotor-router model as an interesting and unique approach to understanding the quantum nature of space and the behavior of particles within it.

(For dual slit experiments go to the related page in this website). The dual slit experiment with rotor-router algorithm is a very interesting alternate way to represent the quantum nature of Space in which the system acts as a whole .

Most of the fun is to discover that the particules can pass through the two slits multiple time. This alternate theory involves a background for momentum interaction.

Here a picture with an additional reflective circle in the center.

flower effect :)

l the RR source is on the left and the absorbing pixel on the right.

As we are on the road to building flowers with the RR algorithm, here one way to build a six petals flower, here the receipt:

-use the UDLR rotor-router.

-add a reflective wall in circle shape; a reflective pixel means that an arriving chip of the RR is sent back to where it just came.

-fill the background to UP direction.

-add an absorbing pixel right below the center (y-1 on the y axis). an absorbing pixel does what is it supposed to do, it eats the chips :)

-launch the RR and wait.

and below, the same output after some more iterations of the RR algorithm. Strange way to cut a pie in 6 !!!

The effect of putting an absorbing space unit adjacent to a chip source in the rotor router algorithm is that it will absorb the chips being emitted by the source. This will affect the overall pattern that is being formed by the chips as they move through the space. It is likely that the presence of the absorbing space unit will cause the pattern around the source and the absorbing pixel to interfere with each other, resulting in a new and potentially unique pattern being formed.

the pattern around a chip source and an absorbing pixel is the result of the interaction between the two, with the position of the arrows on the space units in the grid being affected by the presence of both the source and the absorbing pixel. This interaction can lead to the formation of a new pattern.

One way to continue exploring the rotor-router model is to experiment with adding additional rules to the algorithm. For example, you could try modifying the way the chips interact with the space units or the way the space units are initialized. You could also try adding additional types of space units or modifying the number of output directions for the chips. As you experiment with these modifications, you may discover new patterns and behaviors that provide insight into the fundamental nature of the universe. The rotor-router model is a rich and intriguing tool that offers endless possibilities for exploration and discovery. I encourage you to dive in and see what you can uncover!