>>28025492Okay, so I'm going to keep things simple for this post and go through the assumptions I made about the system and how it would act in practice. Then we can start refining things from there and hopefully catch any misunderstandings I made early on. At first, I defined things in terms of broadness and presence, but since those are negatively proportional to our radius, I'm going to switch to their antonyms, specificity and disparity. These will be represented by the variables s and d and can just be thought of as the respective reciprocals of broadness and presence. All this really does is make the equations easier to read. Our other variables will be r for the radius, h for the height, and V for the volume of a given concept's cylindrical container. We'll also have the constants p for pi and e for Euler's number.
Going back through paragraphsanon's previous posts on the topic, it seems like we want a system where decreasing specificity exponentially decreases the radius, decreasing the disparity increases the height, and the fuel's mass is held constant. I will be using a constant volume in place of mass since that is more easily represented in terms of our variables (V=pr^2h). Assuming a consistent density, this doesn't change anything.
This leads us to our base equations for radius and height: r=de^-s and h=V/(pr^2). The radius equation gives us an exponential relationship between r and s, and the inclusion of d as a factor lets it affect the height. The height equation is just the volume formula solved for h. There's a lot that can be fiddled with in these formulas depending on the exact relationships we want, but they should be somewhat similar to this at their core unless I'm misunderstanding what we want to achieve.
Paragraphsanon also mentioned that the specificity could be assumed constant for a fixed concept while the disparity might change over time. Taking this into account, we get the following derivatives (rates) for r and h: r'=d'e^-s=rd'/d and h'=-2hr'/r=-2hd'/d.
Now let's take a look at some examples. Taking the moon as our concept, where its various phases affect its disparity, we get a smaller height during a new moon which corresponds to a larger radius, and vice-versa for a full moon. This means that chuubanite relying on this concept would have stronger, shorter effects with a new moon and weaker, longer-lasting effects when the moon is full. Since the fuel is held constant, the energy obtained should be the same, but the power and duration will change. I assume all concepts will have the same volume for balancing, in which case none is inherently stronger than another, but some are better suited to certain effects.
Switching our focus to rosestone gives us another example of this in action. I believe it was stated that rosestones normally emit light but can be adjusted to cause sparks and explosions. What this would amount to is changing the glyphs on the chuubanite in order to further specify the concept. This allows you to switch from a low-powered, long-lasting light source to a high-powered, short-lasting explosive.
It also occurs to me that we may not want to enforce such a strict "constant energy output" requirement on our writers, in which case we would need to either drop constant volume (which I imagine could potentially lead to other issues) or have the black-box mechanism which converts concept energy to physical energy adjust things as necessary. In this case, instead of thinking in terms of constant energy with varying power, we would have constant fuel with varying fuel rate.
Paragraphsanon, I was also curious if you had anything in mind when you came up with your original formulas. I didn't really see a way to slide them in at this juncture, but maybe I'm overlooking something. In any case, these formulas are meant to be a base to start from, assuming I didn't misinterpret anything. More factors and variables can be added in as needed, and hopefully we can come out of this with something that works and doesn't make people want to blow their brains out when reading it.
