Editing Template:Actual Age

<noinclude>
{{Obsolete|reason=This template is deprecated as of the fix to growth in [[Version/1.3.3200]].}}

Returns the actual age at which an animal will reach a life stage age listed in its def files.
==Parameters==
*adult_age - this has to be the adult_age listed in the animal's def xml, or seen in the in-game information window
*juvenile_age - if a second parameter is given, the number returned will be the actual juvenile age. This number can only be found from the defs files.
==Formula used==

<code>actual_juvenile_age = (1-1/e^(juvenile_age/adult_age))×adult_age</code>

<code>actual_adult_age = (1-1/e)×adult_age</code>

==Explanation==
If the lifeStageAges minAge values from the animals' defs files were to be believed as-is, you would expect to that horses, which have a reported min adult age of 0.3333, and a reported min juvenile age of 0.25, to be juveniles for (0.3333-0.25)*60 = 5 days. However, the time they actually spend in game as a juvenile is only 2 days. This method accurately predicts this.

The reason for this weirdness is because the amount the growth stat increases at each tick is proportional to <code>1/ticks_to_adulthood</code>, where ticks_to_adulthood is simply the difference between the ticks since birth and the def file's adult_age expressed in ticks. The consequence of growth updating this way is that initially, the growth stat increases at as you would expect, and then as the animal ages, it increases faster, with an infinite growth rate when it's at the adult age reported in the animal's defs file.

{{Graph:Chart|width=200|height=200|xAxisTitle=Age relative to reported adult age|yAxisTitle=Growth|type=line|x=0.0, 0.02, 0.04, 0.06, 0.08, 0.1, 0.12, 0.14, 0.16, 0.18, 0.2, 0.22, 0.24, 0.26, 0.28, 0.3, 0.32, 0.34, 0.36, 0.38, 0.4, 0.42, 0.44, 0.46, 0.48, 0.5, 0.52, 0.54, 0.56, 0.58, 0.6, 0.62, 0.64, 0.66, 0.68, 0.7, 0.72, 0.74, 0.76, 0.78, 0.8, 0.82, 0.84, 0.86, 0.88, 0.9, 0.92, 0.94, 0.96, 0.98|y2=0.001, 0.02121, 0.04184, 0.06291, 0.08443, 0.10642, 0.1289, 0.1519, 0.17545, 0.19956, 0.22427, 0.2496, 0.27559, 0.30228, 0.3297, 0.35789, 0.3869, 0.41677, 0.44757, 0.47934, 0.51216, 0.54609, 0.58121, 0.61761, 0.65539, 0.69465, 0.73551, 0.77812, 0.82262, 0.86919, 0.91804, 0.9694, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 | y1=0.0, 0.02, 0.04, 0.06, 0.08, 0.1, 0.12, 0.14, 0.16, 0.18, 0.2, 0.22, 0.24, 0.26, 0.28, 0.3, 0.32, 0.34, 0.36, 0.38, 0.4, 0.42, 0.44, 0.46, 0.48, 0.5, 0.52, 0.54, 0.56, 0.58, 0.6, 0.62, 0.64, 0.66, 0.68, 0.7, 0.72, 0.74, 0.76, 0.78, 0.8, 0.82, 0.84, 0.86, 0.88, 0.9, 0.92, 0.94, 0.96, 0.98 | yType=number|yAxisMax=1|xAxisMax=1|linewidth=1|colors=red, black|legend=|y1Title=What you would expect|y2Title=What actually happens}}

:An animal becomes an adult as soon as its growth hits 1. From the graph above, it can be observed that this happens when the relative age is at about 0.63. Applied to horses that have a reported adult_age of 0.3333, this relative age of 0.63 occurs at an age of <code>0.3333×0.63 = {{#expr:0.3333*0.63 round 2}}</code>. In fact, this ~0.63 number is <code>1-1/e</code>, where e is [https://en.wikipedia.org/wiki/E_(mathematical_constant) Euler's number].

:A baby animal becomes a juvenile as soon as its growth exceeds <code>juvenile_age/adult_age</code>. For example, horses have a reported juvenile age of 0.25 and a reported adult age of 0.3333, so they become a juvenile when their growth exceeds <code>0.25/0.3333 = 0.75</code>. From the graph above, or from the equation <code>actual_juvenile_age = (1-1/e^(juvenile_age/adult_age))×adult_age</code>, you can work out that the actual age at which a horse becomes a juvenile is <code>(1-1/e^0.75)×0.3333={{#expr:(1-1/2.7182818^0.75)*0.3333 round 3}}</code>.
===Maths===
:<code>with 1 = {sum from [t=0 to actual_ticks_to_adulthood]: 1/(adult_age_expressed_in_ticks - t)},<br>actual_ticks_to_adulthood trends to (1-1/e)×adult_age_expressed_in_ticks as adult_age_expressed_in_ticks trends to infinity</code>

:<code>with (juvenile_age/adult_age) = {sum from [t=0 to actual_ticks_to_juvenile]: 1/(adult_age_expressed_in_ticks - t)},<br>actual_ticks_to_juvenile trends to (1-1/e^(juvenile_age/adult_age))×adult_age_expressed_in_ticks as adult_age_expressed_in_ticks trends to infinity</code>

==Example uses==
*Horse adult: <nowiki>{{Actual Age|0.3333}}</nowiki> -> {{Actual Age|0.3333}}
*Horse juvenile: <nowiki>{{Actual Age|0.3333|0.25}}</nowiki> -> {{Actual Age|0.3333|0.25}}
*Fox juvenile: <nowiki>{{Actual Age|0.3333|0.1}}</nowiki> -> {{Actual Age|0.3333|0.1}}
</noinclude><includeonly>{{#expr: (1-1/2.7182818^({{{2|{{{1}}}}}}/{{{1}}}))*{{{1}}}}}</includeonly>