Week 05

Week 5: Just for Fun by Valzorra

Tech Workshop

Tech Workshop and Building the World was a bit slower this week, as we were having one to ones with James and developing our personal prototypes and little mechanics we may want to work on. In the beginning of the session, while James was attending to other students, I took the opportunity to catch up on some blog posts I had been meaning to do. Once it was my turn for a one to one, James and I discussed what I could focus on for the rest of the day. I expressed interest in the idea of a player having a set of abilities, with the order of the abilities being predetermined. This would mean that the player would have to execute their abilities one after the other based on that predetermined order. At this point James turned around and said that it would be rather premature to begin working on any code, and that instead I should come up with some concept sketches of how these mechanics might work. This was rather useful advice, because it meant I could take the time to properly plan out what the mechanics will do and what they will look like. For the rest of the day I kept drawing a few concept pieces of how they may play out. At this stage, I am not certain whether I will use these abilities for a game, however, I do believe they look kind promising and fun. My work from the Tuesday is attached below. The specific abilities I wanted to explore were a Blinding Light Beam (Number 3), a Defensive Shield (Number 2), and a Teleportation Ability (Number 1).

Friday Presentations

The Friday of Week 5 marked the end of Phase 2, and consequently we were all asked to present the exciting and in-depth research we had done up until that point. This time round the whole process was a lot smoother as we barely ran over time and there were very few technical issues throughout the day. This made everything a lot less draining than last time, and overall I felt like I had more energy to give constructive feedback to most presenters. When it came down to my own presentation, I had a lot of research to go over in a very short period of time. My main goal was to give an adequate summary of all of the work I had done, which unfortunately meant that I could not do justice to the topics I went over. Almost all of them could do with an entire presentation by themselves, however, there is simply no time for that. In terms of feedback, Adam pointed out that the section on Dimension is rather different from the rest of the presentation and that the concepts I described regarding it have been explored in one way or another. Additionally, he recommended that I focus any further efforts in the direction of Data Visualisation or Chance and Probability rather than on the other two sub-sections of Mathematics. Although I believe that the idea of higher dimensions can be explored more efficiently through the medium of video games, I agree with Adam’s assessment that I should avoid focusing on that concept. At that point of the day I decided that I will focus primarily on Data Visualisation and Probability. I also really appreciated the feedback from my course mates as many of them pointed out a few fantastic resources for generative art and other media that relates to the subject. For ease of reference, I have attached my presentation and feedback below.

Later on in the afternoon, I had a one to one discussion with Adam about how to best proceed with work throughout Phase 3. We once again reiterated that I should stray away from working with Dimensions. After that, we debated whether it would be best to proceed with Data Visualisation or with Probability as a major focus. I am rather fond of both topics, so I did not mind developing ideas for both as they are rather interesting to me. At that stage Adam expressed concern than I may not be able to successfully turn the idea of Probability Manipulation into a viable game, at which point I realised I had misrepresented my intentions. I clarified that what I really wanted to do this year was to create a fun and exciting game that features elements of chance and probability simply for entertainment’s sake. What got me into gaming in the first place was the ability to lose myself into an immersive world and to embrace fun mechanics that made me feel joy. It is precisely the playful, yet challenging nature of video games that makes them so incredibly fun, and I just really wanted to work on a project that focuses on those elements of Games Design (for more on my realisation, refer to the first paragraph of Week 5: Game Research Document v0.1).

Once I clarified my intentions to Adam, he was incredibly supportive of the idea, and simply told me to go for it, and to make a fun game. This was a major relief and the dose of encouragement reminded me that I should be having fun throughout this process. There is no point in completely sucking the joy out of the creative process, killing myself working, and trying to solve problems that are simply not there. As has been pointed out on multiple occasions, this will be my last opportunity for a while to devote as much time to a game I want to design and develop. Therefore, there is no point in making this amazing opportunity a painful chore. Rather, I want this project to come from a place of love and passion, both for video games and for mathematics. With this new mindset, I am incredibly excited to begin ideating and to make prototypes for the best ideas I come up with. I am confident that the process will be a lot smoother and less stressful after this reflection.

Week 5: Game Research Document v0.1 by Valzorra

Update: I have finally come to my senses and realised that what I really want to do is to to simply create a fun and entertaining game, which has some exciting notches to mathematics, without taking itself too seriously. I want people to enjoy this experience, to have a fun time, to go on an adventure through its gameplay, to immerse themselves in its world. This project will be a subtle love letter to mathematics, incorporating its principles into its mechanics and structure, while also letting people have fun. With this new mindset, I look forward to going into Phase 3, and exploring dozens of ideas on how to achieve all of this. Now, moving on to the Game Research Document.

The Practice-based Research Game Project Document is meant to be an evolving document of research, thoughts, and design decisions on our game idea, and it will be developed throughout the course of the semester. This is my very first version of the document, and I was only able to actively fill out three main sections of it, the Abstract, the Goals, and the Target Audience. As we progress through the year, the documentation will hopefully continue to be filled and flushed out in more detail. However, for now this is a very brief summary of the key points of my research so far and why I find certain aspects of it rather exciting. Without further ado, enter v.0.1.

Abstract

The study of Chance and Probability is essentially a way of looking into the future through mathematics, which can be incredibly powerful.

Mathematics is an incredibly diverse and exciting topic with an infinity of intricacies, principles, patterns, proofs, all with a watertight underlying logic. It is the essential basis of all other sciences and it finds its way even in fields such as art and design. The abundance of information in the subject meant that I needed to choose a few key focus points within the field to explore further, which was rather difficult as there are numerous topics of interest to me. I am absolutely fascinated by the idea of Chance, Probability, and manipulating seemingly random events through certain rules and principles. That’s why I greatly appreciated looking into things like the Binomial Distribution Formula, Matrices, Markov Chains, and Fundamental Calculus in our Tech Workshop sessions, which I then went on to research and examine further (many thanks to James Stallwood for bearing with me). All of these different methods directly relate to how one can manipulate probability and how to make accurate predictions about the likelihood of certain events from occurring. I find this absolutely incredible, as this means that one can utilise the results from the methodologies listed above to better their decision-making process both in a game and in real life. It’s essentially a way of looking into the most likely future through mathematics. Not only can we peak into the possible future, but we can also alter it through the way we structure data. Maths gives us the power to make decisions based on the results we want, we can transition from the current state of affairs to a desired one with certainty. For example, with Matrices and Markov Chains, one can calculate exactly how much to invest in a marketing campaign in order to get the most optimal boost of clients. This means that Mathematics can help a business flourish through a few simple equations. The same logic can be applied within an interactive environment, it can give users control and hindsight into any seemingly random situation. It’s all about representing data, controlling data, seeing where we are at, where we want to be, and how we shift those probabilities in such a way that we obtain the desired outcome.

Escher.jpg

In the discussion of Markov Chains, and Matrices, I have explored the logical methods by which one can control chance and probability. However, these methodologies require a fairly sophisticated level of understanding of both Mathematics and Functions with Matrices. Based on that, I wondered how one would actually visualise complex data structures in a clear and concise manner. Answering this question lead me to the wonderful world of Data Visualisation, which is an entire field dedicated to these problems. Data Visualisation is about clear communication and ensuring the untrained eye can easily tell what the information is and what the intertwining relationships between its variables are. This is an essential link to the study of Chance and Probability, because once those can be visualised, then they can be altered and manipulated by anyone, even those unfamiliar with the specific mathematical rules. Additionally, Data Visualisation involves thinking about problems from different point of view and perspective, which is entirely what mathematicians do when solving problems. It’s about presenting solutions to problems by looking at them in a different light, about showing those solutions in a comprehensible manner, and about educating on the issues presented. Although the field is quite well-researched, I do believe that more can be done, specifically in three-dimensional Data Visualisation and Data Visualisation in VR, which is largely unexplored.

Data Visualisation: Frequency of Text Messages Within a City

Data Visualisation: Frequency of Text Messages Within a City

Finally, what makes Mathematics incredibly exciting is the idea that the same problem can be looked at from a variety of equally valid fields and perspectives, which could all work together to bring up a solution. Geometric mathematicians may focus on the volume of a coffee mug, those interested in algebra might consider how all of its dimensions relate to each other, the Calculus bunch might want to calculate the instantaneous rate of change on the curve of the handle, while topologists might loudly explain that “This is the same as a donut!“. All of these different professionals offer a very different angle on the same problem, and are all perfectly sound in their logic. I find this diversity, this variety in how you can go about the solution of a problem truly inspirational, and I would love to incorporate that sort of thinking into my design practise. Specifically, this sort of thinking could be well-incorporated into level design and mechanics, so there is the potential for my FMP to turn into a purely mechanical experience. Overall, I am very excited to begin work on a specific project and to carry on with ideation and actually solidifying a game.

Goals

As I have not quite made up my mind on what project to go forward with, I have listed a series of goals I would be happy to achieve this year.

  1. To create a fun game, simply for the sake of fun and entertainment. I would love to create something that people can come home to and enjoy, relax to, and maybe even feel powerful in. I want to create a piece that will that will get people happy and excited, that will form friendly and competitive discussions.

  2. To demonstrate that chance and probability can be manipulated through the use of mathematical formulas and principles. Individuals can predict seemingly random events and incorporate that knowledge into their decision-making process within a game.

  3. To come up with a better way of visualising data and manipulating variables in the third dimension in order to help people better understand information and and its incredible predictive power.

  4. To challenge modern notions of level design and to provide an experience with a series of possible solutions based on the idea of controlling chance events within an environment. To challenge people to think critically about problem-solving and to analyse the level and environment in order to solve it. Hopefully, this would lead to an incredibly satisfying experience.

  5. To improve my own skills in the fields of Level Design, 3D Modelling, Programming and to efficiently incorporate Mathematics into both the mechanics and narrative elements of a game.

Visualising GPS Data From Various Marine Vessels.

Visualising GPS Data From Various Marine Vessels.

User Experience: Audience

Although it is a bit early to say for certain, I would like the Target Audience of the project to be quite wide, possibly Teens and upwards. As I previously mentioned, I want to create a genuinely fun experience with a series of exciting levels that involve or are based around a variety of mathematical principles. The reason I am setting a minimum age of teen/pre-teen is because I do not believe younger children will necessarily be able to appreciate the mathematical logic and principles involved in certain aspects of the game. Additionally, creating a game suitable for everyone means that I would have to restrict myself in some capacity as to the content of that game, which I would not like to do at this stage. If the game happens to involve violence to a certain degree, I would like to have that option available and not tie myself to a universal ranking. However, coming back to the beginning of this paragraph, I believe it is far too early to tell for certain who this project would be most suitable for. All that can be said at this stage is that I would love it to be open to as wide an audience as possible, people from both genders, all sexuality, ethnicity, geographical location, etc. The beauty of mathematics is that it is universal in its logic and it can be appreciated by anyone around the world with basic knowledge of it.

Week 5: Mathematics Visualised by Valzorra

Visualising Probability

We’ve already discussed Chance and Probability in great detail in Week 1: A Welcome Return, Week 2: Calculus and Cancer, Week 3: Research on Mathematics, Week 3: The Matrix, Week 4: Markov Chains, and Week 4: Probability Manipulation in SEO. Although all of that study has given great understanding of how one can control and manipulate probability to make educated and diverse design choices, I haven’t really discussed how Probability is visualised in Mathematics (aside from the Probability Trees discussed with James). In order to visualise probability mathematicians and algorithmic artists turn to Probability Distributions.

The foundation of all Probability Distribution is the Uniform Distribution. In Uniform Distribution there is an equal chance of achieving each result from a certain set or range. For example, with Fair Dice (for more information go to Week 3: Research on Mathematics) we would use Uniform Distribution to visualise the chance of landing on each number of the dice as by definition the chances are equal. Uniform Distribution is also the default for nearly every random() function in programming. It’s interesting to note that when although Uniform Distribution attempts to follow true randomness, it does then to form small clusters and clumps in certain areas. Nonetheless, this Probability Distribution is fantastic for achieving an equal coverage of an area and would be visualised in one dimensional and two dimensional space as illustrated below.

uniform-1d.png
uniform-2d.png

Gaussian or Normal Distribution is extremely popular both in nature and in everyday human activity. In Gaussian Distribution, commonly referred to as a Bell Curve, the data tends to be focused around the centre values with no bias towards the left or the right. In this Probability Distribution, values closer to the mean (which is also equal to the median and the mode) tend to be chosen more often. What’s noteworthy about Normal Distribution is the idea of Standard Deviation, which simply indicates how spread out the values are. Typically, 68% of all values fall within one Standard Deviation of the mean on either side, 95% of values fall within two Standard Deviations from the mean, while 99.7% fall within three. Visually, Normal Distribution tends to focus around the centre, with few values spread out on the sides as shown below.

gauss-1d.png
gauss-2d.png

Another way of visualising probability is through the Power Law Distribution, the most popular of which is the Pareto Distribution. Power Law Distribution is exponentially skewed towards the minimum possible value. These type of Distributions are most commonly used to describe observable phenomena. The most notable example that uses this format is for the Distribution of Wealth in Society as that illustrates how a small portion of the population holds substantial amounts of wealth. Aesthetically, this distribution achieves a good balance between different sized objects. Pareto Distribution in both one dimensional and two dimensional space is shown below.

pareto-1d.png
pareto-2d.png

Probability in Generative Art

The Probability Distributions mentioned above are significant to the way we represent and structure data and to the study of Data Visualisation. However, there are also a number of artworks that take advantage of their properties and logic, specifically Algorithmic Art and Generative Art. Both of those art fields take advantage of autonomous systems such as machines, computers, language rules, genetic sequences, algorithms, and more. Due to the nature of the autonomous systems, the artworks are often created with an element of chance and probability, which can be controlled by the artist or designer to achieve certain effects. The idea of controlling chance and probability through algorithms and mathematics strongly ties into what interests me about the field, which is why Generative Art is perfect visualisation of that concept. Below I have provided a few notable examples of Generative and Algorithmic Art by Tyler Hobbs, which illustrate the field’s relationship to order and randomness, to aesthetics and mathematics. The works below take advantage of Gaussian Distribution and Power Law Distribution in order to obtain a good balance of shapes and density within the works, making them appear clean, precise, yet packed with information.

community5-800.jpg

Data Visualisation

Data Visualisation is the study of the representation of data in the most clear and easy to communicate manner possible. Oftentimes it involves taking vast amounts of data, involving complex and intertwining relationships, and representing it in a visual and digestible format. While Matrices and Probability allow us to manipulate data, Data Visualisation allows the untrained eye to work with that information and understand the contents of a Matrix, for example. There are dozens of different and innovative ways to represent data, both in two-dimensional and three-dimensional space, including Arc Diagrams, Density Plots, Chord Diagrams and many more (for more examples, have a look at Week 2: The Four Themes). Data Visualisation incorporates elements of Graphic Design, User Experience Design, User Interface Design, Mathematics, the Sciences, Art and is all round an incredibly useful discipline for visual communication. Below I have attached a few notable examples and creative approaches to Data Visualisation, which could also be referred to as Data Art. What I find incredibly exciting about Data Visualisation is the idea of clear and concise communication of complex ideas through the power of good design. This is a method of helping people understand information, it can be incredibly educational, and can help train people who have no prior knowledge of the subject matter. Therefore, Data Visualisation is a field worth investigation for both designers and educators.

In the project below, Datamatrics, Ryoji Ikeda has taken enormous volumes of data from computer generated code from software and hardware errors and bugs. All of these errors have then been represented in a variety of two-dimensional and three-dimensional formats. The project is not a traditional use of Data Visualisation as it is actually aimed at representing what can often be the chaotic nature of code and computer software. There has been a later iteration of this specific project, which explored the concept in purely binary values and further reiterated the idea of simplicity and chaos within the realms of technology.

The work below by Marcin Ignac represents the Global Sea Transportation Network is entirely based on the paths of sea transportation vessels and their actual GPS Coordinates as they travel around the world. This project is especially connected to Matrices as the data from those GPS Coordinates would be recorded within a Matrix. Therefore, this is a terrific example of how Matrices can be presented in a very easy to understand and digestible format, allowing for more clear communication of the data. What’s more is that by adding new routes and new matrices within this system, it would be incredibly easy to observe changes and estimate where certain ships are meant to be at any given time.

paths.png

Platonic Solids Transformations

I have gone into detail over the Platonic Solids and why they are exciting in some of my previous posts (Week 3: Research on Geometry, Week 3: Research on Mathematics). However, what’s even more interesting is that they can actually be used as the basis for a near infinite number of other complicated shapes through the use of Geometric Transformations. I found a fantastic tool online created by Marcin Ignac, which can edit Platonic Solids to create a multitude of more complex shapes. Some of the techniques used in the tool include splitting the faces of the Platonic Solids into triangles, changing the heights of those triangles. Additionally, shapes can be merged together, their faces and geometric properties working in combination with each other to create a new solid. Overall, the tool is an absolutely fantastic demonstration of Transformations within three-dimensional space and what’s more is that any figure can also be exported as an OBJ. There transformations can be turned into separate mechanics and functions within a game, making the tool and the mathematics behind it a method for idea generation. I highly recommend exploring the Platonic Solids Editor as it provides valuable insight into many of the geometric properties discussed throughout the blog.