Hi,
I have been working with processing and I can make some 'cool' stuff. but thats as far as i can go. Ok not entirely tru, I can still manage to learn from other peoples code, which is also good.

but then what i would really love to do is bring my own original ideas on paper. meaning, I know exactly what i want, but find it hard to figure out the math behind it.

For instance, I can learn how to make sandpainters from Jared's code, but when I read the code, I find it hard to figure out how he got the equations like:

point(ox+(x-ox)*sin(sin(i*w)),oy+(y-oy)*sin(sin(i*w)));

- Does this happen through trial and error?
- Are there any known mathematics or physics that I am not aware of?
- or is this pure genius at work ?

Coming from pure design background, things like these could be daunting and I am trying to make my way through it and learn as much as I can, so any help or suggestions are greatly appreciated.

Thanks a lot.

ssdesign, i feel you man. im in the same boat. math is like that part of your dinner you eat last, leaving most of it on your plate...

ira's book does go into the most detail "mathematically" of the three processing books.

shiffman's website, "nature of code", has some nice paragraphs about math, too.

i thought i saw another processing book that will be published later in the year dealing with "algorithms".


-0.

Hi Ira,
Thanks, your book is on my list to purchase

I think there must be something more out there which is more about mathematics of iterative painting or something like that.

I found some of the javascript code from spirograph very useful.

Some meta-stuff on learning and coding maths. To start, don't ever expect that the process will go like this:

1. Learn the math

2. Code.

In my case, this is what really helps:

* review anything I've forgotten or can't quite remember. (For a lot of us, maths is a muscle that wastes - if you don't use it every day, you'll probably find you need to go back and figure out e.g. what that 'sohcahtoa' thing was good for again!)

* Try using pen/pencil and paper. After a while, some stuff you'll just be able to code - but old fashioned pencil and paper is really helpful, at least for me. Armed with Google, pen, paper and Processing you should be able to learn a lot of what you need.

* Have a document (I just use Word) that you can use for combining planning and whingeing. A kind of geek field diary. I can't code without doing this: I use one section for bullet-pointed pseudocode and another for venting and figuring out where I'm trying to get to.

* Write up your final coding solution in your code comments. Aim for concise but thorough. You will thank yourself later (and other people will like reading your code too.)

* If you're coding a function with many parts, it may help to start by separating them into smaller variables first: you can stick it all into one line (as below) later once you know each part is working.

An example from my last experiment:

http://www.personal.leeds.ac.uk/~gy06do/processing/ces_function

meshPoints[l][k] = pow( (a* pow( ((inputMax/float(meshSize))*k), p ) + ((1-a) * pow ( (((inputMax/float(meshSize))*l)) , p)) ), (s/p) );

Bleurgh! This was from an equation that I'd entered in Maple, which - as you'll see from the code comment - looks like:

(a*k^p+(1-a)*l^p)^(s/p)

Which is a CES function:

http://en.wikipedia.org/wiki/Constant_elasticity_of_substitution

Don't worry about what it does. The point is, the line I took through learning the function and getting to a code version of it was slow. This is rarely emphasised in stuff you read: if you're not used to it, it can appear that you're expected to read maths just like English and code it like some kind of math-channelling wizard. Not true. A great guide here:

http://web.stonehill.edu/compsci/History_Math/math-read.htm

To quote:

"Reading mathematics too quickly results in frustration.  A half hour of concentration in a novel might net the average reader 20-60 pages with full comprehension, depending on the novel and the experience of the reader.  The same half hour in a math article buys you 0-10 lines depending on the article and how experienced you are at reading mathematics. There is no substitute for work and time.  You can speed up your math reading skill by practicing, but be careful.  Like any skill, trying too much too fast can set you back and kill your motivation."

That last point is spot on: don't expect too much of yourself or you'll lose motivation. Go slow. And be thankful for Processing, which is an exemplary way of learning maths and coding!

thanks for the post Dan_Olner.... some good tips in there.

Back in the Dark Ages, when I had the free time of a high school student and my CPU was measured in kilohertz rather than gigahertz (think about that for a second), I did a lot of dinking around with plotting math formulas.

Sounds geeky, but there wasn't much else you could fit into the computer in those days.

So, I did lots of experimenting with polynomials and trig functions, just to see what would happen.  Just to see what cool patterns I could put onto the screen.

Trig functions are a very fertile ground for experimentation, because their inherently cyclic nature leads to lots of repetition.

You learn quickly that the point (r*cos(theta), r*sin(theta)) is a circle. But circles get boring.  

So what happens if you add ANOTHER trig-set on top of that?  What does (r1*cos(theta1)+r2*cos(theta2), r1*sin(theta1)+r2*sin(theta2)) produce?  What happens as you change the relative rates at which theta1 and theta2 advance?  What happens if you turn r1 and/or r2 into functions of theta also?

The variations are endless.

After a while of doing this, not only have you had a lot of fun but you also develop an intuitive sense for how to turn an idea into math.  You start to say to yourself "I'll bet if I changed the formula like _this_, it would look like such-and-such."  And you turn out to be right.

You'll develop to the point where you start asking yourself questions that are beyond the math you know.  That's when you hit Wikipedia to learn (or in most cases, re-learn stuff you've forgotten since high school or college) about the pythagorean distance formula, how to calculate the distance from a point to a line, how to calculate the slope of a line or the tangent of a curve, and on and on.

You'll be learning new math in service of a piece of art you want to create or a problem that you _want_ to solve, which is a wonderful experience that is absolutely not present in the classroom setting of solving problems because they've been assigned as homework.

Personally, I love maths, although maths doesn't like me.
I mean that my mind isn't very good at handling very abstract stuff, it is a visual mind. High level maths I (tried) to learn in (preparation) school after baccalaureate (certificate got after 18) were mostly high over my head.
But simple maths manipulated in Processing: arithmetic, trigonometry, geometry, statistics, etc. are OK. It can become harder with 3D or physics, but it isn't so hard.
What is nice with Processing is that you are able to quickly visualize the maths, see if something is wrong, play with formulae, tweak them, etc.

Your example, using a sine of sine, looks more like an experiment (what if...) than a real world formula, unless I miss something, which is probable anyway...

Looking at my local library, I saw a number of accessible math books, showing them in a playful side, with lot of illustrations and simple terms.
Don't feel silly to get them and read them, I am sure they can help a lot, and are the entry point for more complex books. And hey, at a library, if the book doesn't please you, you just bring them back and try another!