Difference between revisions of "Template:Actual Age"

Revision as of 15:08, 30 September 2021

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 must be found from the defs files.

Formula used

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

actual_adult_age = (1-1/e)×adult_age

Explanation

If the lifeStageAges minAge values from the animals' defs files were to be believed as-is, you would expect that horses, which have a reported minimum adult age of 0.3333, and a reported minimum 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 1/ticks_to_adulthood, 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.

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 0.3333×0.63 = 0.21. In fact, this ~0.63 number is 1-1/e, where e is Euler's number.

A baby animal becomes a juvenile as soon as its growth exceeds juvenile_age/adult_age. 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 0.25/0.3333 = 0.75. From the graph above, or from the equation actual_juvenile_age = (1-1/e^(juvenile_age/adult_age))×adult_age, you can work out that the actual age at which a horse becomes a juvenile is (1-1/e^0.75)×0.3333=0.176.

Maths

with 1 = {sum from [t=0 to actual_ticks_to_adulthood]: 1/(adult_age_expressed_in_ticks - t)},
actual_ticks_to_adulthood trends to (1-1/e)×adult_age_expressed_in_ticks as adult_age_expressed_in_ticks trends to infinity

with (juvenile_age/adult_age) = {sum from [t=0 to actual_ticks_to_juvenile]: 1/(adult_age_expressed_in_ticks - t)},
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

Example uses

Horse adult: {{Actual Age|0.3333}} -> 0.21068578097385
Horse juvenile: {{Actual Age|0.3333|0.25}} -> 0.17587203545609
Fox juvenile: {{Actual Age|0.3333|0.1}} -> 0.086392694342281

@@ Line 16: / Line 16: @@
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-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 = 0.6</code>.
+: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>