My thinking here is that although transcendental equations don’t have algebraic answers are there still links between them? That theory is supported by the contour lines in the following  So I wasn’t going to look into this but sometimes I just get captured by the mathematics. I have known for a while that most equations can’t be solved. The unsolvability of most equations leads to transcendental numbers. Numbers which aren’t the result of a solvable algebraic equation like 5x+1=7 or 2x^2=3 but can be computed, at least approximately. These numbers include pi and e. There isn’t a formula for pi or e, we can define them, we can even define them without the use of geometry. As I have found out in my curious investigations both numbers seem to crop up only when calculus is involved. e is the solution to the problem of The functions that produce these two have always seemed arbitrary to me. Why is it the case that when we don’t know the answer to we just say, the answer is the answer? We

DRY - Don't repeat yourself One of the things I did wrong when I started to write software for a career is to try and optimise before I had a chance to understand. Having worked a little longer I feel I have a better appreciation for what should be automated and when.  There are a lot of things that I felt I was repeatedly doing that according to my understanding of the DRY principles at the time, I thought I should be abstracted away, so as not to have to repeat myself. I kept telling myself that if I was finding a project boring that the boredom was a notification from my mind that there is unnecessary repetition. I still feel that there is a level of truth in the idea of boredom being the mind picking up on repetition however I now realise that is that there is a level of repetitiveness that is inherent in working as a software developer. That is not to say that we shouldn’t strive to remove the repetitiveness but that the job of a developer when working on a project must be fir

From the jsfiddle here I have done a previous post on gradient noise , explaining my realisation at why the equations involved are what they are. Hydronics are notoriously challenging in procedural landscapes because very few realistic ontogenetic algorithms exist. The solutions employed by the likes of dwarf fortress is to run calculations based on a path at different levels of detail down from the mountains to the oceans. Given that gradient, noise is so-called because it makes use of gradients and from the simplicity with which beaches can be generated I wondered if a simple -1/a trick would yield path perpendicular to the beaches - a river? The reasoning behind -1/a is that if you have a gradient on a graph, say “a” from a line ax+b, if you want a perpendicular line, then the gradient will be (-1/a). Following this reasoning, and the fact that we have the gradient at each point, I attempted to calculate the negative inverse of the gradient, which ended up being fiendishly complicat