"Dying off" germs aren't dying off fast enough.

Game version: LU-366134

Confirmed, seeing exact same behavior in gas.  Dying in gas is -29% and is much faster than 'dying off' which seems to be a fixed -3/s rather than the -367% it is supposed to be.

^{video has been increased to 20x speed}

A decay rate of 367% per cycle, as worked before, naturally means that you reach 100% dead in less than a cycle. The most obvious interpretation is that it means you hit all dead at 600/3.67 = 163s, about a quarter cycle.  That half-life, then, is approximately 6 seconds or 0.01 cycles.

When a half-life is being used, or equivalently a percentage dying per unit of time, the number of deaths per second is an exponentially decaying curve. This is reflected in the e^-t (or 0.5^t/thalf) term in the half life equations. In contrast, a fixed death rate is linear: a graph of population vs time is simply a straight line, with a negative slope equal to the death rate (i.e. 3 deaths/second is simply a slope of -3).

This change has other weird effects - you can take 2000 kg of gas in a single tile, with say 18000 germs and 10 cycles to die off at -3/s --- and let it expand into a 10x10 room, and now your die-off rate is, in aggregate, -300/s and you're germ-free in a tenth of a cycle. In fact, spreading a gas or liquid into a bunch of very low-volume tiles is about the only way to get them clean of germs now that this absurdly slow rate is introduced. Of course, for food, that's not even an option.

I'm certain this change was unintentional and you should restore the -367%/cycle rate for 'dying off'. 
----
If, however, this change was intentional:

Then you still have a bug. In that case, it is wrong to report any half-life whatsoever once the 'dying off' state is reached, since the state is governed by linear, i.e. not exponential, decay. When quantities decrease following a half-life, the half-life itself remains constant, while the decay rate itself changes in proportion to the remaining population. Instead, you're now holding the decay rate constant at -3, which means the time to cut the population in half constantly changes, which means there is no actual half-life value to report.

And indeed, I have a square of gas with 18,000 germs with a fixed death rate of 3 per second -- that's 1800 per cycle, or 10 cycles to complete death or 5 to reach 9000 germs remaining. The game is unsurprisingly reporting an incorrect 'half-life' time of 7.8 cycles at this instant, though it is constantly decreasing. Critically, it would still be incorrect if the game was reporting a "5 cycle half-life" -- because after a single half life, the time for the population to be halved again would then be only 2.5 cycles, and then 1.25, etc.

The fact that the calculated half-life constantly decreases is simply further evidence of why it's wrong. If the time to halve the population constantly changes, then you don't have half-lifes at all. That's the meaning of the term, and is why the answer to "what's the half-life of plutonium 241" is "14.4 years," not "it depends on what the population* is right now."  

*number of atoms in your hunk of metal

Edited September 19, 2019 by tofof

On 9/18/2019 at 7:54 PM, tofof said:

Game version: LU-366134

Confirmed, seeing exact same behavior in gas.  Dying in gas is -29% and is much faster than 'dying off' which seems to be a fixed -3/s rather than the -367% it is supposed to be.

^{video has been increased to 20x speed}

A decay rate of 367% per cycle, as worked before, naturally means that you reach 100% dead in less than a cycle. The most obvious interpretation is that it means you hit all dead at 600/3.67 = 163s, about a quarter cycle.  That half-life, then, is approximately 6 seconds or 0.01 cycles.

When a half-life is being used, or equivalently a percentage dying per unit of time, the number of deaths per second is an exponentially decaying curve. This is reflected in the e^-t (or 0.5^t/thalf) term in the half life equations. In contrast, a fixed death rate is linear: a graph of population vs time is simply a straight line, with a negative slope equal to the death rate (i.e. 3 deaths/second is simply a slope of -3).

This change has other weird effects - you can take 2000 kg of gas in a single tile, with say 18000 germs and 10 cycles to die off at -3/s --- and let it expand into a 10x10 room, and now your die-off rate is, in aggregate, -300/s and you're germ-free in a tenth of a cycle. In fact, spreading a gas or liquid into a bunch of very low-volume tiles is about the only way to get them clean of germs now that this absurdly slow rate is introduced. Of course, for food, that's not even an option.

I'm certain this change was unintentional and you should restore the -367%/cycle rate for 'dying off'. 
----
If, however, this change was intentional:

Then you still have a bug. In that case, it is wrong to report any half-life whatsoever once the 'dying off' state is reached, since the state is governed by linear, i.e. not exponential, decay. When quantities decrease following a half-life, the half-life itself remains constant, while the decay rate itself changes in proportion to the remaining population. Instead, you're now holding the decay rate constant at -3, which means the time to cut the population in half constantly changes, which means there is no actual half-life value to report.

And indeed, I have a square of gas with 18,000 germs with a fixed death rate of 3 per second -- that's 1800 per cycle, or 10 cycles to complete death or 5 to reach 9000 germs remaining. The game is unsurprisingly reporting an incorrect 'half-life' time of 7.8 cycles at this instant, though it is constantly decreasing. Critically, it would still be incorrect if the game was reporting a "5 cycle half-life" -- because after a single half life, the time for the population to be halved again would then be only 2.5 cycles, and then 1.25, etc.

The fact that the calculated half-life constantly decreases is simply further evidence of why it's wrong. If the time to halve the population constantly changes, then you don't have half-lifes at all. That's the meaning of the term, and is why the answer to "what's the half-life of plutonium 241" is "14.4 years," not "it depends on what the population* is right now."  

*number of atoms in your hunk of metal

This verification is amazingly detailed, good work.

I can confirm this with slimelung "Dying off" in Chlorene.

Furthermore, they "Dying off" effect due to low germ count completely stops dying off at any reasonable rate around 200 germs or so.