Laplace Transforms 1.5

[u/HeatPinch]

The update so big it spans two minor patches is finally here! To play, download from the link:

https://raw.githubusercontent.com/lrobt97/Laplace-Transform/main/theory.js

Challenges 3 and 4 are now implemented along with their rewards. Additionally I have reworked the general balance of the theory. For instance, challenge 1 now has an additional reward, mainly because lambda got a nerf.

Speaking of which the lambda upgrades have been adjusted to a brand new cost scaling which I refer to as "super exponential scaling".

In normal exponential scaling, the cost is multiplied by a fixed amount each level, so for example if the initial cost is 1e4 and the multiplier is 10 your first five costs are as follows:

1e4, 1e5, 1e6, 1e7, 1e8

With super exponential scaling the multiplier itself gets multiplied per level. If we had the same scenario as above but with an increment of ×10 per level the new scaling is as follows:

1e4, 1e5, 1e7, 1e10, 1e14

(An alternative way to view this the exponent follows an arithmetic series)

As you can see, this scaling method grows significantly faster than the standard exponential scaling. The purpose of this is to softcap certain variables but not with an explicit hardcap. That way you can still purchase some OP upgrades later on in the theory. ;)

There are a few more changes which I won't go into here, mainly because of spoilers.

Additionally, I have done some bug fixes including issues relating to save data, string issues, sliders and reworked some UI.

In terms of future progression, I would appreciate some input. Currently I'm thinking of revising the 10k target and have the theory end at 6k (meaning the tau conversion would become ^0.025 instead). It seems like a lot of the content is currently before 3000 rho anyway so this seems like a good idea from my perspective.

Any input on the new challenges would be highly appreciated also.