Monday July 26, 2010

Mathmatics and Art

Maths and Art is one of our papers this semester and it looks to be pretty intense. It replaces Intro to Creative Technologies. Our first class, we were given a run down of what to expect and our assignments. I'm going to keep Maths and Art as a separate entry from the studio entries so that it can be documented properly as this paper is going to be quite an exploration.

The aim of the paper is is to develop an understanding of both Maths and Art and explore interdisciplinary creative practice between them.

We'll explore history and various contexts of art and basic concepts in maths.

We'll also be doing a lot of research - reading of texts from libraries and academic resources and honing our academic writing skills too. Aside from the lectures and tutorials (and own research), we will have a literature review - That is a culmination of our research efforts, an Essay - Our own arguments based on the review and a Practical Project which I can't really go into yet and I'm a bit hazy on it.

We also had an outline of the rest of this semester and it looks both daunting and exciting and interesting. This semester instead of 4 Studio projects, we will be given 2. They will be broader scope, and we'll be able to use previously learnt skills but we will also be learning new skills and software in order to complete the projects. There will be more to them but we'll have more time as there are only 2.

The 3rd paper, Design and Data Structures will be like the short but intense Programming for Creativity, this time we'll be learning C and writing an application for an iPhone. Because of this (and the fact that I'll be busy anyway) I'll hold off from further self-directed learning in that subject (I might revisit it at some point though). Instead I might dedicate my spare moments (not that I'll really have any) to some more PHP learning and mySQL, because I have a website idea that I want to execute, and I'd kind of like to either write the site from ground up or know enough to pull apart an existing CMS and customise it to my needs - I doubt there is a CMS off the shelf to do what I'm planning. Also I've been trying to watch one video a night (failing half the time though) from Khan Academy on Mathematics. The plan is to work my way through all the videos on various maths subjects and become rather good with maths.

Footnote. You have got to be kidding me! The sidebar puts this label "10" directly under 1. Yes I know how that works and why, I just expected better. Spoilt by current generation OS's (even Windows finally) that order numbered lists correctly. I need to fix it soonish...

    Monday August 2, 2010

Art History

Our second lecture for Mathematics and Art was an overview of Art History. We had been given some reading material in preparation for our literature review and it occurred to me that understanding the history of Art may be rather crucial to understanding any further reading on the subject. Once again a topic that has always interested me but I have never formally (or informally) studied it. I didn't really know how to start, it seemed that there were so many movements in the last couple of hundred years and any time that I've ever read descriptions of different movements it's almost like another language. And they always reference each other. How are you supposed to learn about anything that defines itself by reference to other parts of itself?  It's like looking up in a dictionary the word "design" and getting "a product of creativity" then looking up "creativity" and getting "a part of design".

But it turns out that it's really not all that complicated and the hard bits are hard for most people and it all comes under a broad definition anyway. The very definition of Art has changed with the Post-modern movements, and I'm not sure where I sit currently opinion-wise. Art has been a trade, a science and a creative pursuit. It's also more recently been commentary. But Art can now be just about anything. I'd go further into this but I'm currently developing my thoughts on the subject.

    Monday August 2, 2010

Math and Geometry.

Today we had our first Math lesson in our Mathematics and Art Paper. A new lecturer and we were introduced to some open source software written in Java called C.a.R. C.a.R stands for Compass and Ruler, it simulates whatever you can do with a compass and a straight edge along with more advanced functions. We learnt the 5 axioms of Euclidean geometry which are basically 5 "common sense" rules that no one tries to prove (heavily paraphrased for simplicity):

  1. A line exists between 2 points.
  2. Any line segment can be extended.
  3. A circle consists of one  fix point (the centre) and one point that is constant distance from that fixed point.
  4. All right angles are congruent.
  5. Any point outside of a line can only have one line going through it that is parallel to the original line.
From there we constructed parallel lines, right angles and intersections using only a ruler and a compass. Except we did it in C.a.R, not with an actual ruler and a compass. I'd have found an actual ruler and a compass much easier actually. This is all basic technical drawing that I learnt in 4th form. Although in my head a stronger connection was made between this geometry and radians, which is something I ignored when I was at school, not being interested in maths in the slightest. I'm interested these days.

We also touched on the Golden Ratio which is the idea that 1.618....(an irrational number) is an easily calculated and plotted geometrical construction that also happens to look visually pleasing. As such lots of ancient buildings are built to this ratio.

What I've been pondering so far is how Art in the Maths and more widely the Science world seems to be regarded as what I'd call design. There seems to be some attempt to connect the two worlds but it assumes and old definition of Art. I'm really not sure how one can give any mathematical meaning to post modern art unless one was to look at chaos theory or... something. Also everything I have read so far talks about beauty. To me art is not necessarily beautiful by any definition. I don't just mean aesthetically although it seems to me some of the simpler connections are only talking about aesthetics but I also mean in terms of unifying anything. Anyway, while art may once have been about aesthetics, it's certainly not always the case now. Aesthetics is more of an applied art like design, and usually for commercial reasons.

    Sunday August 15, 2010

Truth and Proof

Back to an Art lecture, we explored the difference between Art as a representation of what we perceive as the truth (what we see) and Art as an abstraction of truth. That is, when art stops becoming a representation of reality and it becomes it's own reality. We explored realism and expressionism and reproductions on truth. It was actually an interesting concept but I'm not doing it justice here. I guess I don't fully comprehend it to the level of being able to break it down into a solid explanation, which is what I'm a fan of doing. As I said right at the very beginning of this blog, if you can't explain it simply, you don't really understand it. Some of the concepts we touch on are a bit up in the air and it's up to us to pursue the subject further using what we've been shown so far. The plan for Math & Art was to spend the entire Monday on the subject but so far we've fallen into the trap of finishing up class then going back to the studio to do more of our Cinematic Flaneur Project. If I ever find the time I will come back here to explain the concept more fully.

    Tuesday August 17, 2010

Matrix and Transformation

Our Math's lecturer walked us through the basics of Matrices and transformation. The Maths component is something I'm really interested in learning about although I found this lecture quite frustrating for a number of outside reasons. It takes a lot of concentration to understand our Maths lecturer as English is not his first language. This of course doesn't bother me, but that in combination with the fact that half of the class are not interested in maths means that it slowly gets a bit noisy. Which only makes it more difficult to understand. I briefly considered telling my class to shut up or leave I was so annoyed, although this might not have gone down very well. The concepts that we covered were not even difficult and I was familiar with them, and as soon as it seemed we were about to move to the next and more interesting level (rotational transformation of a matrix) it was time to vacate the lecture theatre.

We did however reconvene in another room but did not go back to rotational transformation but a pile of exercises creating golden shapes. This I found tedious but stayed in case we suddenly covered new ground.

I'll look up rotational transformation myself, If I'm right, this is an incredibly interesting topic and one some of my class mates (if anyone in the class reads this... you do??) apparently interested in building 3D games in the future would do well to try to understand, as it's the basis of 3D space in those games.

    Monday August 23, 2010

Beauty and Aesthetics

This lecture wasn't too full-on as half of the class didn't attend. Our first assignment (a Literature review) was due at 4pm and also The following day our Studio hand in. We'll then be spending the next 2 weeks (I think) doing our next paper on XCode.

[I'll cover the subject in more detail later....]

Related, this weekend wound up being for most of the class the weekend they did their Literature review. Unfortunately I was just as disorganised. Well, it wasn't just plain disorganisation, it was related to not really knowing how to do the research part properly in conjunction with having a studio project that was also quite demanding yet so much easier to make tangible progress in. The result for me and many others is a Literature review hashed together the night before. I'm told that this is a fairly normal thing for students to do by a friend who has been there and done that. At least first year students. I find it pretty unacceptable to work like that but at least this time, being my first induction to the whole academic writing thing, it's probably understandable especially given that just about everybody does it.

I up skilled massively this weekend, learning how to research my subject in an academic fashion (it's not quite the same as real-world methods) and actively reading, and of course then came the lamenting "If only I'd done this last weekend". Of course last weekend I was mucking around with video footage.

The word limit was low (1500-2000) and the question was fairly simple: In what ways can the creative practice integrate both math and art? If I'd been asked this question and just expected to answer off the top of my head I'm fairly certain I could have come up with 1500 words of examples. Perhaps. Or perhaps if I'd tried, I'd discover my ideas are actually quite vague. Either way my job was to pull current writings on the subject and compare and contrast them. If I was to do this again I'd do it well, as now I suddenly have the understanding of how to do such a thing. I will use these skills in the future. But for this literature review those skills are not apparent. What I submitted was truly awful. It's embarrassing really. As time started to run out, I was increasingly aware of my lack of sleep and with 2 hours for deadline I just did not care anymore. My last 3 paragraphs are mere sentences, the conclusion is short and weak and half way through my references went out the window.

But I'll just have to deal with it and do better next time. Most of the class are also unhappy with their submissions, so I'm in good company.

    Tuesday August 31, 2010

Image Processing

I don't feel like I'm having much luck with classes at the moment. I sat in on the maths lecture and we got back to matrices and matrix multiplication. I now know how to multiply 2 matrices, one will be 3x2 and the other 2x3, and we'll get a result that is 2x2... I really have no idea about the logic behind such a thing and what on earth the result is good for. How can you possibly apply the calculation of two matrices that don't line up and the result being a 3rd matrix that doesn't resemble either of the 2 multiples... to anything? So this is something I need to look into at some point...

Actually I do remember this from 4th or 5th form maths, it made little sense then too. Honestly, this is the problem with maths and the way it's taught in schools. It's never applied to anything and often makes no sense. Maths could be an interesting and engaging subject and people could learn and understand it, and want to do so. They could remember it. But not with the way it's commonly taught. I just don't understand why it has to be so problematic.

Small anecdote: Straight after I finished 7th form, I borrowed a book, the 1st year text on Psychology and I read it from cover to cover. In that book was a break down of basic statistics, the bell curve, 95th percentile as it was a key to understanding certain studies. It was so easy to grasp and I vaguely remember being taught the very same thing in maths 3 years earlier and not really making much sense of it. But a book on entirely different subject made it easily accessible. For a start it was because it was for a purpose. Maths classes generally don't give you a reason why you'd want to know something. The situation could be vastly improved if students were given small projects in which they had to discover they needed a certain math to get something done. Then told how to do it then they actually got to use it. Also if it was taught from a historical perspective, how did theorems get discovered or devised and why? What practical problems did they solve? But maths will continue to be a boring irrelevant subject until the day past students find they need to know something in order to do their computer science later in life or whatever, and at that point they will learn with great stress or fail or if they are lucky, discover one of the few resources that isn't awful. At which point I may as well suggest Khan Academy for anyone struggling with math.

We then moved back on to rotation calculations that we'd dropped off from 2 weeks ago. Once again I'd like to explore that further, now I know the formula. I want to understand it. Even if I am 20 years too late from needing to know how to translate a vector by hand. Next I'll find out how 3D space is translated onto a 2D plane. It's the kid in me, it fascinated me once.

We then had an explanation of how a matrix related to a bitmap image and image capture devices. I personally found it painful to listen to, with the urge to take over and explain the bits that always get left out. Things like just why maximum luminance is such an odd number like 256 (It was mentioned that it's because it's 2^8, but if I didn't know what I know I'd still be asking "So???"). I went home later on and worked on my Stopwatch.

Anyone in my class reading this (it's alright, no one does), short version is: computers use binary number system because it translates well to on and off, (decimal would mean 10 different voltages to represent 10 digits and that would be prone to errors). So base 2 number system (binary) means that every number to the left of the first digit is twice as powerful as the bit (binary-digit) to it's left as opposed to decimal where we have Ones, Tens, One-Hundreds etc. So it's Ones, Twos, Fours... 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024... numbers look familiar? Your usb stick is 8gb, 16gb or 32gb for example? Well there ya go there is the reason. So one byte is 8 bits, and converted to decimal = 256. Why is a byte 8 bits? Because years ago Intel produced it's first microprocessor and it could do calculation on 4 bits (later on with a hint of humour called a nibble) then it quickly released a machine that could do 8 bits which was a number that was starting to be usable for most common purposes: 8 bits (256) shades of grey... 256 steps of amplitude(volume) in a sampled wave form... The English alphabet, numerals, punctuation and a bunch of control codes fit into a byte (8 bits, 256 decimal) and it was called ASCII...

24-bit images are 3 bytes, and they contain one byte representing the luminance of Red, one byte of Green, one for Blue 3bytes = 16.8 million colours. 32-bit images have an extra byte representing the alpha channel which is how transparent a given pixel is.

Or it's CMYK is which is another colour space called a subtractive colour space and used for printing. Then there are High Dynamic range images that are 16-bits per pixel (2 bytes) so they are 48-bit images. While they take up twice the file size, 16 bits=65535 levels of luminance so much much higher fidelity colour, - very important if you are going to muck around with images in photoshop as do so usually results in dropping data from the image. 256 is low fidelity in audio too, and CD quality is 16 bits per sample... 44200 times a second - 44.2khz16-bit, - ever seen those numbers around CD discussion?

All this stuff is good to know in many ways, not least because this is a technical degree and not knowing this stuff might otherwise be considered laughable and someone not to be taken seriously. Understanding the basics gives you a grounding in the more complex stuff and can help you in ways that you don't know yet. Like any knowledge you can draw from it in ways you cannot imagine. Plus it's a bit weird to do colour correction in After Effects but not know this. I mean, really, how does one do that?


Right that felt better I think I filled in some of the missing bits...

    Tuesday September 28, 2010

Image Processing II

For the first time this course I consciously decided to not go to a lecture. Well I've missed a few classes here and there, moving house, in bed with the flu, but this time I just looked at what we were doing and decided I'd rather get a tooth pulled.

I don't think I'd have learnt anything new, but it's difficult to ascertain what was taught from other class members who's main recollection is that it was 3 hours. Converting CMYK to RGB aand back was the most sensible answer I've had. Of course however that was done (probably inverting CMY and working black calculation in there) it was done without recognition of real-world factors such as colour management and UCR which are more complicated and... we have software that does it.

I got my literature review back later in the week and it was as awful as I said it would be. Well, I passed by a margin which surprised the hell out of me, but then I saw other people's work and they passed by a higher margin so I guess being our first attempt at academic writing we got off lightly. This will be the worst mark I get in this course.

    Wednesday September 29, 2010


I feel like I've been a bit whiny lately in this blog. Math and Art has been the first majorly challenging thing on this course, and it's really quite easy stuff. Part of it is my lit review mis-step. The essay/practical looks somewhat daunting now as I don't think it can really stand on the shoulders of the Lit review. Not too much of a problem but I have to get creative and I'm not feeling very creative at the moment. The essay is meant to articulate the maths and the creativity behind whatever it is we are exploring. And reference other artists and mathematicians. My abstract was a bit general, though this could work in my favour I suppose. A lot of people seem to be exploring music and while I find that appealing myself, if everyone else is doing it I'd rather be a bit different. Also, the current Studio project is audio-based, I think that there is more potential for confusion of the two than them building on one another.

The Essay is worth 25%.

The Practical we'll be doing in tandem and it;s worth 50%. We are to produce a work or a body of works integrating math and art, demonstrating our experimentation with what we have chosen to explore. And document it. Explaining what is asked of us has helped me understand it a bit more too... which is why I came here really.

But I have so much reading to do tonight for Studio and tomorrow I'll be editing audio for a presentation (which will be blogged about next). This weekend will be dedicated to the Essay. I just hope we don't get landed with anything else.

    Friday October 8, 2010

Essay II

Monday we had another Maths & Art lecture, and I felt slightly duped. I came in expecting an art lecture and discovered maths. We covered symmetry. Again.

It might be partly the class's fault, as an observation on the state of affairs in regards to maths was pointed out to me by a classmate. No one answers questions, so perhaps our lecturer interprets that as no one really understanding what is going on. Which is not the case, they understand, they are bored with the slow-paced progress. While sitting in class I observed something else I've started to recognise. If a lecturer is not engaging enough, they may end some statement with a question. Listeners only recognise it as a question after it becomes apparent that the talker is waiting for a response. Except they don't know what the question was.

It was only an hour as we had tutorials later in the day. Tutorials are occasional smaller classes (we're divided into 4 groups) where we get to discuss issues relating to to the subject. This was our opportunity to discuss our essay and practical with each other, critique or suggest ideas and run our own ideas by our peers and our tutor.

I had a couple of ideas, one based off an article that I read about whether video games can be art. It seems like a strange question to ask, and it was sent by a friend who plays games (and drives me batty in the process), but it was rather interesting. I decided that I could create a small game, it would involve maths and create art. It would attempt to model nature in the process. This is because my abstract asked stated that both maths and art attempt to model or represent nature and that maths and art were essentially part of nature itself (met with some disagreement by my tutor as art is a social construction). Another idea I briefly had was to move back into music, as I've seen some absolutely brilliant maths equations turned into tunes (and visuals) more here. It turns out that there is already a whole genre of art games. But as I've said before we're already doing an audio-based studio project, although it's more about sound than music.

But sitting through other people's ideas I started to think about how little time we have and I feel like I'm over complicating it. Maths and Art combined in a creative practice is second-nature to what my previous "career" was. Illustrator, Photoshop etc are all mathematical programs used to produce works of art (and other graphics of course). I started to formulate the possibility of writing a filter similar to a Photoshop filter. I ran the Artgames thoughts and the filter idea by my tutor who suggested that the two aren't that far apart and I could write a game of sorts that manipulates images in some way. I think I'll go with that.

    Thursday October 14, 2010

Essay III

We were given an extra week to complete our essay which was just as well. I had planned to spend the week nights researching and writing what I could but instead wound up doing Project 6 homework. So the weekend was to be my time but I spend much of it away from home and a computer coming to a friend's aid. Today, (Monday) we didn't have a lecture, but instead our tutor was to give one-on-one sessions to anyone that needed some more input. Instead I've concentrated on reading up on my topic. I've started with Wikipedia to get an overview of art-games, interactive art , and popular game titles that had no specific goal.

The game Alien Garden is mildly interesting because it reminds me of various experiments that I have read about in the past where software mimics evolution for the purpose of experimentation or even applications such as producing a better design or better code than a programmer can. All quite interesting, I don't have any links at the moment. But it takes me in a possible new direction. It also integrates my abstract well (maths and art imitating nature), which I was prepared to re-write but if I can tie all of this up it would be better as it's mildly interesting.

Hmmm, that is a good point "interesting". I need to stop thinking of this as some difficult assignment and more as a personal project whose exploration I find interesting. That way I can probably claw my way back to feeling smug about being able to do this instead of rather daunted and also confused as to why it's so daunting. I've been looking forward to writing an essay for... years really. I always thought I'd be good at it. I get my chance and for some reason I'm not so confident.

    Tuesday October 19, 2010

Maths and Art Final Essay

Despite my intention to not follow in the footsteps of the literature review, I never really got much of a chance to write the essay until the weekend. But at least it was much easy to write and reach the word limit.

I just started writing somewhere in the middle then kept writing then later arranged it and added a conclusion and an introduction and tied it all up. Not as well as I might have liked, on the bus home from handing it in on Monday I reflected on it and thought it was a bit simplistic. There is so much detail I could have gone into. But then again 1000 to 1500 words is not a lot of space once you have enough ideas.

Also, two thirds of the way through I re-read the brief to see if I was on track and decided that in some ways I wasn't really. It specifically asked for minimal quotes or discussion from other sources. But I needed to add so much background. Perhaps if I'd known where I was going in the literature review I might have added appropriate material there and then put my reading of everything in the essay as asked. But I wont be too hard on myself, it was my first go at this sort of thing, it's hard to know where one is going when the information about what we are doing is staggered out while I could always improve my time management, I was busy with studio work.

I found it easier to write this time because I relaxed about the "academic writing" thing. I wrote slightly more to my personal style although more formal. I don't care if there are more learned people who disagree, I find academic writing that no one can understand a bit poncy. What's so difficult about writing in a style that is easy for a lay person to read, and why is it bad if you are still presenting complex subject matter? Until this question can be answered satisfactorily I'll remain sceptical about some of the intention behind academic writing.

Anyway, a friend just pointed out to me that I am supposed to upload the damn thing to this blog as well as hand it in. So everyone can see it, ugh. Here goes:

Oh btw, I don't play videogames, I can't stand them. So I'm not looking for some weird justification of them personally. Makes it more fun to argue for them actually.

Maths, Art, Nature, Video games.


Mathematics and art to the uninitiated seem to be about as distant subjects as they can possibly be, however this essay will attempt to connect them on multiple levels. One can possibly imagine Mathematics as a tool for art of the renaissance, using perspective and ratio, further diving into other obvious arts such as music and architecture in which mathematics is a fundamental part of keeping a functional piece of art standing. We will explore how maths is used to simulate nature to create works of art that represent nature. We will do this by looking at video games. The reason video games have been chosen is because of recent controversy regarding the subject, and whether they can in fact be an art form. We will start with some background on this controversy.

Video games as Art?

In 2005, respected film critic Roger Ebert answered a question from a reader in regards to whether video games can be considered art. He responded, part of which was “I am prepared to believe that video games can be elegant, subtle, sophisticated, challenging and visually wonderful. But I believe the nature of the medium prevents it from moving beyond craftsmanship to the stature of art.”1

In August 2009, game innovator Kellee Santiago gave a TED talk 2 opposing Ebert’s view, saying that games are already art, citing three experimental games as examples. One was called Waco Resurrection, that took the form of a Role Playing Game (RPG) where the player first had to don a mask of David Koresh, then announce “I am David Koresh”. The player has to cast spells using their voice in-game. The game is in “total chaos” through out, and difficult to navigate. Kellee describe the game as an expression of the developers not of what really happened in Waco, but what happened in “culture and society as a result”.

Another example was an Xbox 360 game called Braid, that explored the player’s relationship with their past by allowing them to rewind time every time they die, and follow a story as the game continued. The third example called “Flower” explored the relationship between an urban environment and nature by tracking the progress of a flower seed blowing in the wind which controlled by the player.

While poor examples, Ebert was motivated to respond in a blog post 3 in the Chicago Sunday Times and label them as “pathetic”. To date, there are over 4730 comments to his article. At about 4500 comments, he responded with another blog post entitled “Okay, kids, play on my lawn”. 4 In the post he conceded two main issues:

One is that he did not play video games and was not interested in doing so. Therefore was probably not qualified to comment.

The other point was that he had never provided a definition of art. To this he supplied a definition from the Oxford Dictionary of English:

“[noun] the expression or application of human creative skill and imagination, typically in a visual form such as painting or sculpture, producing works to be appreciated primarily for their beauty or emotional power: the art of the Renaissance | great art is concerned with moral imperfections | she studied art in Paris. | art, fine art, artwork, creative activity. • works produced by such skill and imagination: his collection of modern art | an art critic. • creative activity resulting in the production of paintings, drawings, or sculpture: she’s good at art.

One game in particular was mentioned multiple times according to Ebert, “Shadow of the Colossus” for Playstation 2. Shadow of the Colossus has been described as a work of art, 5 it is an unusual game with nothing to explore, just a wasteland, forcing players to paint their own picture as to why it became this way.

Art’s various definitions

The definition of art is problematic. It has changed as art has changed. An early attempt was made by Greek philosopher Aristotle, he defined art as an imitation of nature. This raises several issues in regards to modern art that is not representational in a conventional sense. It really seems that no single definition can be arrived at without excluding at least one form of art. For the purpose of the project accompanying this essay however, Aristotle’s definition very useful. The project will be a video game that will produce art by modelling physical laws of nature. However the project will still work if one is to use the Oxford definition. The quality of the art will to at least some degree be controlled by the player.

Another one of Ebert’s criticism of video games was that games by nature gave multiple scenarios and kept a score. You had to win a game. To this end, the project game keeps no score, as there is nothing to score. Winning is producing a piece with interesting quality.

Interactive Art

Art installations that have some form of interactively involved have increased with the advent technology, in particular digital programmable technology. But interactive art is not always so apparent.

In October 2010, reported an installation by Tao Wells, an artist who explains that he has been on the unemployment benefit “on and off since 1997”. 6 His piece is called ‘The Beneficiary’s Office’ and it urges people to abandon jobs that they dislike rather than suffer ‘slavery’. Controversy has surrounded the piece as it is part of a $53,000 performance installation series, and Wells received $2,000 for the piece. The reaction it has generated with public in various forums is a form of on-going interactively and arguably part of the piece.

This is mentioned as it is an intermediary step between art which one may for example hang on a wall and look at and art that contains some form of gadgetry to create an interactive experience. It also seems that while interactive art installations are often a personal experience, or shared by those few people around one, Well’s statement involves the entire society up and down the country, anyone who will chose to participate. Much like a video game community.


A fundamental part of all video games is mathematics. Even for a most basic game, that written in a high level language, the creator will be confronted with a way of keeping the score. At lower levels, computers are machines of logic and pure mathematics is taking place every second. More complex games will require collision detection of on-screen elements of some sort, and the majority of games released today are in 3D environments. The mathematics involved simply drawing a successful 3D environment include an algebra, geometry 7 such as understanding of co-ordinates and vectors, matrix transformation and projection into a 2D co-ordinate system (the screen).

Added to simply rendering a 3D environment, one needs to create some degree of realistic physics. Objects need to detect collisions, not simply pass through each other. They need to fall with gravity. Objects need difference forces acting on them and energy needs to be transferred so that an objects inertia changes as it does in the real world, providing it is the real world that is being simulated. Physics is then taken a step further in rendering as light and reflections are calculated to simulate real-world conditions.


In order to model reality, nature, or a version of it, one requires multiple types of mathematics, from simply describing objects, their space, physical laws and interactions and light ray tracing. This simply cannot be avoided in the creation of video games or modelling of nature on a computer. It is fundamental. From there, using computers and mathematics as a tool one can concentrate on higher concepts such as the aesthetic of the game, and what it is expressing. Essentially one can use mathematics to produce a work of art.


  1. Ebert, R.   (2005, November 27).   Why did the chicken cross the genders?.   Retrieved from
  2. Santiago, K.   (2009, March 29).   TEDxUSC - Kellee Santiago - 3/23/09.   Retrieved from
  3. Ebert, R.   (2010, April 15).   Video games can never be art.   Retrieved from
  4. Ebert, R.   (2010, April 15).   Okay, kids, play on my lawn.   Retrieved from
  5. Roper, C.   (2005, October 17).   Shadow of the Colossus Review.   Retrieved from
  6. Nicholes, L.   (2010, October 5).   The Dominion Post.   Retrieved from
  7. Dunn, F & Parberry, I.   (2002).   3D Math Primer for Games and Graphics development.   Wordware Publishing, Inc.   Retrieved from

    Tuesday October 26, 2010

Maths and Art Project

Prior to handing in my Essay I'd gone to the library to look at a book recommended to me - Physics for Game Developers, which was in the High Demand section which means you can't take it out, it can only be read inside the library. So I spent about an hour skimming the book but it was a bit complex. It assumed highschool physics and mathematics, and I did do both up until 6th form (year 12?) but that was ages ago and if truth be told I bombed both anyway (extraneous factors). Pretty pictures though and one in particular was enough to get me thinking about particle systems. Particle systems are simply a form of modelling liquids and gases by giving physics to lots of particles. However the picture that caught my interest was using particles to model cloth. They were all connected so could not stray away from their neighbours, but they could move around within that constraint. So this got me thinking, but with the Studio project, thinking was as far as it went for a while.

I wanted to model blobs of paint being thrown at a wall or dropped or... something. This would require some 3D work. The plan was to use Processing, which we had used in Semester 1's Programming for Creativity paper, but I've never used the 3D functions. They are easy though, all the 3D projection is done for you. But still, I hasn't sure how this "game" was going to look.

The day before the performance I found the time to go back to the library and check out another book that was on the library catalogue that I noticed could be taken out. Physics for Game Programmers came with me for later reading. It looks like a really good book, although one I didn't really have time to read, I read the first chapter and finally learnt what ∑ means (apparently I should have known this from highschool). the first chapter also covered other maths symbols, greek symbols, coordinates and systems, matrices, matrix multiplication and rotation and differential equations. Everything I'd hoped to learn in Maths class this semester in about 6 pages.

But I had to just start doing, as time was running out. This greatly annoyed me. I would really like to spend a couple of uninterrupted weeks actually exploring this project properly. There are loads of factors at play here, but the only one I can attempt to do better with is some form of time management. I'm not alone, it seems to be a common story but it's annoying, as the briefs often convey how one is to experiment and explore a subject over time but the reality is to cram as much work into the thing with the closest deadline then cram the next thing then the next. Not so much exploring done over a period of weeks.

On Monday (and a public holiday) I helped a classmate film their project and in return I was given some advice and pointed in the direction of a physics library written for processing. The advice, well, perspective, was that I don't have to go inventing the wheel to get the job done. I don't have to write all the physics myself (given the time) when other people have already done that. I just need to use what is available. It's like wanting to drill holes so building a drill. What is the point. Toxiclib was the name of a physics library that could model liquids.However while browsing processing libraries I also came across MSAFluid library, a library for solving real-time fluid dynamics simulations. This sounded interesting too so I browsed the various demos and simulations from both libraries and decided to change my project a little bit. Rather than splattering blobs of paint, I decided to use the particle system in the Fluid Library to model paint of some sort.

It took a couple of hours to do the most basic thing - install the libraries in processing. Where are the instructions for this? I wound up discovering that on my own. I then spent several hours picking through the code and simplifying it, taking out bits that I didn't need so I could understand it better. This took until the hand-in day and I encountered part of the rendering in OpenGL code and couldn't quite understand how it worked. If I could just have had a couple more days to spend on this on it's own (and not be interrupted by outside things as was the case all weekend). Also the API reference was a bit iffy. I'd love to have picked apart the source code (in Java) for the library and just re-implement a version of it in my processing program, but... time...

But I started to realise that the concept had been sort of proved. It wasn't quite a game yet and lacked controls that I wanted to implement such as a colour picker and physics adjustments along with ability to save images. But it did use maths to model fluids (nature) and was capable of producing (questionable) art. So I used it and took screenshots and burnt the program and screenies to CD and handed it in. I considered briefly working on it more and handing it in again but... I'm over it. I want to get the other submissions due in the next week and a half done instead. Below is an example of what it produced, it's been coloured in photoshop, in it's current state it only produced white dots (which would later have looked more like liquid if I'd had the chance).

swirly pattern