Resources cycles

Resources in Eykar have different behaviours when extracted. Here's the mathematical basis behind these behaviours.

The world of eykar allows the extraction of different types of resources. Some resources (called renewable) regenerate if they are not exploited. This is for example the case of fish. Other non-renewable resources, such as iron, can be extracted in finite quantities in a plot and become harder and harder to extract as time goes by.

This model is not perfect but should be realistic enough to add challenge to the game. See criticism for more information.

Common calculation

Parameters

Δt, the delay in seconds since last extraction q, the previously remaining quantity max_q, the maximum quantity which can be stored affine_growth linear_growth extraction_speed affine_extraction linear_extraction

Algorithm

1) Computing the new quantity

new_quantity = max(q * linear_growth^Δt + affine_growth * Δt, max_q)

Example:

Quantity evolution in function of Δt with q=200, linear_growth=1.002 and affine_growth=-0.05

2) Compute the extraction

extracted = min(extraction_speed*(affine_extraction + linear_extraction*new_quantity), new_quantity)

3) Return results

q <- new_quantity-extracted

extracted <- extracted

Criticism

There are two main criticisms. The first is that if growth is exponential, it simply stops at its maximum heading when it is at its maximum growth. A sigmoid or even a function that oscillates after reaching its maximum would be more realistic.

The second is that the extraction is instantaneous. In reality, if you send a huge number of fishermen out on a long fishing trip lasting several days, their presence should reduce the population faster than it grows, and they could potentially come back with little result. Here, the fishing is done after the population has increased (and potentially reached its maximum level) and ends immediately.