In Dark Forest, energy sending is a very important part, through the energy sending between planets that the dazzling attack and defense battles are formed, and energy sending can also carry silver and artifacts, it is energy sending that makes the universe come alive. But we don't know much about the mechanism of energy sending.
First of all, when sending energy, the energy that eventually arrives will decay as the distance increases, and when we select a planet in the universe, several circles will appear.
The code for calculating the arrival energy in Dark Forest is as follows：
Converted, this is basically the following formula：
We can see that the final energy arrival is related to four factors: the amount of energy sent, the distance, the Range and the energy limit of the planet.
Suppose we are given the energy sent, then as the distance increases, the curve of the final arrival energy is as follows.
From the graph we can see that as the distance increases, the energy decreasing trend becomes more gentle, and more importantly, two 50% energy sends, the final arrival energy is less than 100% send, which means that small energy sends should be avoided as much as possible. As we mentioned in the previous article, the optimal percentage of energy sent is about 80%, when the final arrival energy is not far from 100% and allows the planet to quickly enter a high-speed energy recovery period.
Let's change the perspective and assume that the energy sent is increasing, then the distance curve can be reached as follows.
As we can see, as the energy increases, the increase in the maximum distance that can be reached slows down, that is, there is a marginal effect, so it is not necessary to send all the energy of the planet. Another thing we can notice from the graph is that the Distance is much greater than the Range distance of the planet. Range does not represent the farthest distance the planet's energy can reach, which is a very confusing point, Range is just a measure of the distance the planet's energy can travel. The farthest energy can reach is 4.3 times the Range, which is log2(20). after doubling the Range, the same distance, the energy reached will also be doubled, so raising the Range will not only improve the range of the planet's energy, but also the energy that can be reached.
