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Disclaimer: This is a simplified version of the guide. The guide will skip over things, and is not completely optimal. Click here for a more polished, in-depth, and optimal guide.
When discussion strategy, this section may use more jargon then the rest of the guide. If you are confused, please check out the discord server and ask.
Thanks to Mathis S for help with this guide
Without reading this overview, a lot of the equations will seem completely random and nonsensical
MF is based around the Magnetic Field equations, the equations that govern the motion of a charged particle in the sinusoidal field. This theory simulates the movement of a charged particle with mass \(m\) and charge \(q\) in a solenoid of infinite length with current \(I\) and a density of turns \(\delta\) creating magnetic field \(B\).
A solenoid is a type of electromagnet formed by a helical coil of wire whose length is significantly greater than its diameter. When a current of electricity is passed through it. Our solenoid in this theory has properties that are determined by our upgrades.
For this simulation we consider a particle starting at position \(x = 0\), and time \(t_s = 0\), with an initial velocity given by the \(v_i\) purchasable variables. Due the the magnetic field created by the solenoid effecting our particle, it moves in a helix like pattern with a constant \(x\) velocity and \(\omega\) angular frequency, a measure of how much it spins around in the helix pattern (rad/s). Because of this, buying \(v_i\) variables will have no effect until the simulation is reset and the new initial velocities can be applied
Furthermore, MF is the first theory to implement a second prestige layer, by having a prestige layer below publications. This new prestige layer is representative of "resetting" the simulating and applying the new \(v_i\) conditions, which does not reset upgrades but does reset the particles \(x\) position by resetting \(t_s\) to 0
$$\dot{\rho} = Cc_1c_2\omega^{4.1}x^{3.2}v^{1.3}$$
$$v = \sqrt{v_x^2 + v_y^2 + v_z^2}$$
$$x = v_xt_s$$
$$B = \mu_0I\delta$$
The value B above represents the magnetic flux density, which is (simplified) a measure of the strength of a magnetic field
$$\omega = \frac{q}{m}B$$
$$v_x = [v_1v_2 \times 10^{-20}](t_s = 0)$$
$$v_y = [v_3v_4 \times 10^{-18}](t_s = 0) \times sin(\omega t_s)$$
$$v_z = [v_3v_4 \times 10^{-18}](t_s = 0) \times cos(\omega t_s)$$
$$\dot{I} = \frac{a_1}{400}(10^{-15}-\frac{I}{a_2})$$
$$m = 1e-3, q = 1.602e-19, \mu_0 = 4\pi \times 10^{-7}$$
That's a lot of equations. The most equations I've seen in a custom theory that actually matter. Luckily, most of it is just a bunch of multiplication, so it is not that complex. C is an arbitrary balancing term that changes with milestones
Also, you may notice this term: \((t_s = 0)\). This means that this equations is not always true. It "updates" to become true then you reset the
particle, setting \(t_s = 0\). For instance:
$$v_x = [v_1v_2 \times 10^{-20}](t_s = 0)$$
This question determines that \(v_x = v_1v_2 \times 10^{-20}\). However, purchasing \(v_{12}\) will not have an immediate effect of \(v_x\) - instead
it will only update when you reset the particle, and reset \(t_s\).
As explained in the overview, this is because the \(v_i\) variables represent the initial conditions of the magneti field simulation, and thus have
no effect until the simulation is reset
Finally, there is an equation that should look familiar from t5 $$\dot{I} = \frac{a_1}{400}(10^{-15} - \frac{I}{a_2})$$ This is the logistic function equations we saw in T5, however it some crucial differences:
With this knowledge, we can simplify the equations - although in doing so we must abstract away from the physical representation
$$\dot{\rho} = Cc_1c_2\omega^{4.1}x^{3.2}v^{1.3}$$
$$\omega = 4\pi \times 1.602e-23 \times I\delta$$
$$\dot{I} = \frac{a_1}{400}(10^{-15} - \frac{I}{a_2})$$
$$\dot{x} = v_1v_2(t_s = 0)$$
$$v = \sqrt{v_1^2v_2^2 + v_3^2v_4^2}(t_s = 0)$$
The above is for low \(\omega\) making \(sin(\omega) \approx 0\)
Or even simpler, assuming continuous particle resets, and merging all constants - a method that allows us the analyse the effect of each variable in a vacuum
$$\dot{\rho} = Cc_1c_2I^{4.1}\delta^{4.1}v_1^{3.2}v_2^{3.2}t_s^{3.2}(v_1^2v_2^2 + v_3^2v_4^2)^{0.65}$$
And thus the variable breakdown
| \(c_1\) | Increases \(\dot{\rho}\) by 10.5% |
| \(c_2\) | Increases \(\dot{\rho}\) by 2x |
| \(a_1\) | Increases \(\dot{I}\) by 15% |
| \(a_2\) | Increases I cap by 1.25x, and thus \(\dot{\rho}\) by 2.5x |
| \(\delta\) | Increases \(\omega\) by 1.1x, and thus \(\dot{\rho}\) by 1.48x |
| \(v_1\) | Increases \(\dot{x}\) by 7% (requires reset) |
| \(v_2\) | Increases \(\dot{x}\) by 1.3x, and thus \(\dot{\rho}\) by 2.32x over time (requires reset) |
| \(v_3\) | Increases \(v\) by 7% (requires reset) |
| \(v_4\) | Increases \(v\) by 1.4-1.5x and thus \(\dot{\rho}\) by 1.62x (requires reset) |
Strategy in MF revolves around the central question: When should you reset the particle? Resetting the particle as we have seen is a tradeoff between the short term (decreases x immediately) and the long term (higher \(v_{1234}\) = higher x & v later on). Of course, you do not want to reset too often, lest you never let \(t_s\) build, but you also do not want to reset to rarely, and lose out on higher \(v_{1234}\).
No hard and fast strategy has been proven best, and many people do their own way, but I recommend the strategy made by d4Nf6Bg51-0: (No names have been assigned as of yet)
Purchase \(v_{1234}\) and reset when:
Purchase \(v_{1234}\) and reset when:
For variable purchasing, you should follow simple doubling strats
| \(c_1\) | Cost is 10x less then \(min(c_2, a_2)\) |
| \(c_2\) | Always buy |
| \(\delta\) | Cost is 2x less then \(min(c_2, a_2)\) |
| \(a_1\) | Cost is 10x less then \(min(c_2, a_2)\) |
| \(a_2\) | Always buy |