# Mathematics

"In a way, Art is a theory about the way the world looks to human beings. It’s abundantly obvious that one doesn’t know the world around us in detail. What artists have accomplished is realizing that there’s only a small amount of stuff that’s important, and then seeing what it was. So they can do some of my research for me. When you look at early stuff of Van Gogh there are zillions of details that are put into it, there's always an immense amount of information in his paintings. It obviously occurred to him, what is the irreducible amount of this stuff that you have to put in... But to say there’s a piece [of cloud] over here with that much density, and next to it a piece with this much density—to accumulate that much detailed information, I think is wrong. It’s certainly not how a human being perceives those things, it’s not how an artist perceives them. Somewhere the business of writing down partial differential equations is not to have done the work on the problem... Somehow the wondrous promise of the earth is that there are things beautiful in it, things wondrous and alluring, and by virtue of your trade you want to understand them.

## Quick Post: Sum Table

If you have an array of values, how can you take the sum of any range of them in constant time? With a sum table! Here's a formal definition: Given a list of values , then a sum table is a corresponding list such that . That is, each value in the sum table is […]

## Real-Time Clouds Pt 2: The Actual Cloud Part

Update: The source can be found on GitHub. In part one of this thrilling diptych I unveiled my beautiful classic noise function on the world using many many lines of someone else's code. Well in this post I hope to further bedazzle you by actually using that noise function-- and even some of my own code. […]

## Real-Time Clouds Pt 1: A Study of Noise Functions

Update: Part II of this post can be found here. Update 2: The source can be found on GitHub. Where to begin? As a previous post pointed out, I've been working my way through "Texturing and Modeling: A Procedural Approach" and it's blowing my dang mind. For instance, did you know that Scorched Earth is […]

## Spherical Terrain Generation

Update: part 2 here. I posted a terrible demo a few weeks ago of a geosphere with some procedural mesh perturbation-- then I ran off and never explained it. Then, in my last article, I finally walked through the magic behind geospheres. In this article, I refined my approach to spherical terrain generation and finally […]

## Geosphere: Revisited

Update: At long last, the SO answer has been found! Added a link. Lately I've been shrinking my goals so that I can actually reach them. I mean, I'd rather have fifty small projects that have all been completed than ten large ones that haven't (you wouldn't believe how many things I have 90% completed […]