Coordinate field

Coordinate field is a big set of random points, uniformly distributed on a plane. When Coordinate field is influensed by Psi, the points density deviates from the average in some areas, creating anomalies, that can be statistically detected.

## Theory

In order to get a point on the map from quantum noise, we must first transform it into a coordinate field. Based on the perturbations of this field, we will look for the place indicated by the MMI effect. A coordinate field is a set of points evenly distributed throughout the map. In reality, these points are scattered on a simple plane surface, and a ready-made result of calculations is projected onto the geographic map (i.e., the system contains no actual information about the real world location, it is working only on a coordinate plane). Moreover, in order for the calculations to be statistically reliable, the field must be sufficiently dense, that is, several thousand points must be scattered over the map, which requires a lot of entropy, and, consequently, fast REG.

The main idea of making a coordinate field is to accumulate Psi-induced deviations as an emergent trend among multiple iterations. One point here is a single iteration and it may contain a small deviation in it, for example, the point is slightly moved towards a certain location. If we will repeat the point generation 10000 times, we will be able to find this deviation among them by fluctuations of points density.

But how exactly do we get coordinates from a random series of ones and zeros? There are two methods for converting random bits to coordinates:

**Binary Word (BW)** - this method is currently used on the Randonautica server, as it is the fastest and does not require too much entropy. The method is that 32 bits are simply taken from the entropy stream and translated from the binary code directly into a decimal number. From two such numbers, you can get the coordinate (x, y). Thus, for 10,000 coordinates, approximately 80Kb of entropy is required.

We will not cover all the mathematical problems that arise with this number generation method, such as Modulo Bias, but we will consider a number of problems related directly to MMI.

One of these is the **bit significance problem**. In a series of bits that form a number, the first bit will always affect the position of the coordinate more than the last. For example, let's take the number 214 (11010110) and change the first bit (01010110): we get 86. But if we change the last bit in it, (11010111), we get 215. That is, the first bit changed the number by almost 2.5 times, and the last one only by a single unit. Given that the intention can change any bit in the series, such an influence of its position on the result is highly undesirable, not to mention the fact that we will get a completely different set of coordinates if we start reading the entropy not from the first bit, but from the second, for example.

To get around this problem, multiple solutions was suggested, such as using 2D-Gray Codes. Another solution suggested was a bit-rotation method, where the entire bitstring from REG passes through a 32-bit window, shifting 1 bit to the side at a time. Thus, each shift gives a new number, and each bit goes through all positions, participating in the generation of 32 different numbers. Unfortunately, bit-rotation was found to create an autocorrellation bias, where highly regular patterns like 10101010 have bigger probability to replicate during bit-shift. By this reason, the method was reworked into Channels Method, where we use a bit-sequence to create 32 channels with corresponding amount of bit-shifts and then select the most successfull one by measuring deviations in it.

Another problem is **information density problem**. To hit the exact target point, BW should have 32 bits being flipped by Psi of 32 bits in a Word. Thats extremely improbable, so we assume, that we have a lot of patterns with errors, where some bits are flipped, and some aren't. Thats also where bit significance problem hits again and the Gray Code come in handy.

**Random Walker (RW)** - is the main alternative to the Binary Word method. In this method, we initially create the required number of points with coordinates (0,0), and then, depending on which bit we get from REG, we shift the coordinates of each axis by one up or down / left or right. Thus, the coordinates "wander" and scatter from the middle of the plane in random directions. However, when they disperse, their distance from the center will have a normal distribution, that is, there will be more points in the middle, and fewer at the edges. To turn them into a uniform coordinate field, the coordinates of the points are converted to z-scores by dividing their coordinates by the square root of the number of steps, and then converted to uniform coordinates using Cumulative distribution function.

The advantage of this method is that it does not have the problem of bit significance and can accumulate a large amount of statistical deviation in every single point. So even if we have only 1 per 100 bits flipped by Psi, it will effectively contribute to points location. But the method also has disadvantages. The most important of these is that the accuracy of the z-scores into which normally distributed points are converted depends on the number of steps they take while random-walking. This accuracy, in turn, affects the resolution of the points after being converted to a uniform distribution. That is, if the points have taken a few steps, then the coordinate field will look like a square grid with large gaps between points. And to get a coordinate field with the right resolution, we need to take hundreds of thousands of steps for each point, which requires an insane amount of entropy and very long calculations. For example, the 900\*900 map wil require 170000 steps for each point and coordinate field of 5000 points will require more than 200Mb of entropy.

We're currently trying to solve this by making RW-BW hybrid solutions, that are currently in a process of research. Also to test efectiveness of those solutions, we need to create a certain standard of MMI-influence, that is, a source of intention that could influence REG constantly and without interruption. A person is not able to focus attention for a long time without getting tired or distracted, so the developers of the Fatum project placed their hopes for creating such a standard on plants. Some experiments show that plants are capable of MMI. To do this, installations are created where REG controls the lamps that illuminate the plants, and they have to influence it in order to get more light.