Week 06

Week 6: Project Proposal 2 by Valzorra


While researching Probability and Chance, specifically how to visualise the concepts, I came across a series of works in the field of Generative Art and Algorithmic Art (for more information, refer to Week 5: Mathematics Visualised). Looking at those striking images inspired me to think about an experience where one is completely surrounded by Generative Art and where one’s interactions with that environment continuously change it. For the most part, Generative and Algorithmic Art does not involve any interactive elements, but rather is restricted to either a static image or a short film. Therefore, Generative and Algorithmic Art could be elevated to a new level of interaction through the medium of video games. Additionally, I believe that there is more to be done in the field of Abstract Art Games and the ideas they could convey through algorithms, shapes, and form, so this project would provide a great way to explore that idea.

Project Overview

The project would essentially be a VR walk-through experience that allows the player to interact with its environment. Based on those interactions, the environment would change in accordance pre-determined mathematical functions, many of which would be based on Calculus (for more on that, please refer to the my work during Tech Workshop). As we have learned from Markov Chains and Matrices, in order to make procedural change, we oftentimes need a starting state. As the player transitions from their starting state and interacts with the environment, the environment will get continuously more abstract, changing with every movement, every touch of the player, based on functions like Probability Distributions, the Reimann-Zeta Function, Sine and Cosine Functions, and more. That’s the basic overarching goal and premise of the project, now on to the specific locations the players will explore.

Once they enter the experience, players will be placed in a tunnel like structure. This tunnel will be shaped to echo what the inside of the spine may look like. Within this tunnel, players will be able to walk, jump over obstacles, touch its walls, go up and down the tunnel in any way they please. As they progress through the tunnel and explore it’s structure, the environment will change with each movement and touch. Each action will have a mapped function to it, and those functions would then be applied to the tunnel, changing its shape, its course, even potentially destroying the tunnel. The experience will slowly transition from a detailed environment to an increasingly abstract and low-poly world. Finally, the player will reach a large open space, almost like the centre of the skull, where they will be able to look at and reflect on the changes they have made within the environment. That’s why each experience through this tunnel would be unique to every player. Additionally, this connects to a series of universal themes and ideas that would make the project that much more thought-provoking. It ties into the idea that actions have consequences, that everyone’s life path is different and those differences must be appreciated. It displays how mathematics is the underlying construction of the universe through an artistic medium. It would also connect to the idea of reflection upon one’s actions and how focusing on the big picture rather than the small details can sometimes be more revealing than anything else. Another exciting point about this project is that I believe it could work terrifically in a Virtual Reality Environment.

Concept Pieces

This would be an incredibly visual process, with no fixed narrative experience. Walking through the tunnel would generate a visual story and trace of your actions and movement. I have not created my own sketches of the concept as of yet, however, I have attached a series of images that will hopefully help convey how this may look visually. The first image below is a good example of how the space may look when the player first enters. I have not made any decisions in relation to colour just yet, however, that would be the overall starting shape of the tunnel.

Annihilation, 2018

Annihilation, 2018

As the player progresses through the tunnel, they will inevitably create patterns of trajectory, they may touch certain objects within, they might pick things up or destroy parts the environment. Based on those actions, the landscape of the tunnel and path may continue to change in ways such as the ones displayed below.


As the player progresses through the environment further, its shape and outline will continue to change based on the predetermined set functions. It will inevitably get continuously more chaotic, more abstract and as previously mentioned, the world may even collapse on itself at that stage.


At the end of the experience, the player will have a moment to reflect on all of the changes they have caused within this environment, which may end up looking something like the image below. This moment of reflection will allow the player to appreciate what their actions have caused in this world and whether or not they like what they see. Hopefully, it may also encourage people to reflect upon their own lives and consider whether or not they are happy with what they have so far. The question to follow would be if it’s too late to change or if things can be restructured.


Week 6: Project Proposal 1 by Valzorra


While I was researching Markov Chains and Matrices, I explored the concept of On-Page SEO, specifically what variables contribute to websites ranking higher in search engines. The conclusion of my analysis was that one can give numerical values to the key On-Page SEO Factors, and then estimate what changes need to be implemented to achieve the ranking one wants. In simpler terms, we can figure out what to change to rank higher based on where our site is at and where we want it to be (for the full analysis, please refer to Week 4: Probability Manipulation in SEO). However, although I have explored the relationships between the variables, their relative weights, and how they could fit into a Markov Chain, this process can get quite technical. Many website owners and publishers are not necessarily familiar with Matrices and Markov Chains, so the knowledge of how to improve their performance would require unnecessary training in a field that’s irrelevant to their work. However, I believe I may have found an answer to this problem through a new methodology for Data Visualisation (which is closely related to my research on the topic, found in Week 5: Mathematics Visualised). What’s more is that this method does not necessarily need to be limited to SEO, but it could rather be a universal visual training tool, which would mitigate the issue of working with raw numbers.

Project Overview

Most methods for Data Visualisation take place in two-dimensional space, such as histograms, point graphs, arc diagrams, and more. These techniques are quite efficient when working with a very limited number of variables and when the relationships between them are straightforward. However, it would be rather difficult to depict more complex and intertwining information. For example, On-Page SEO Factors roughly fit into three major categories, with a series of three to five subcategories, all of which affect each other differently. In order to represent this complex information, we need to take it into an additional dimension. By representing the data in three dimensions, we gain access to a series of solids, with a variety of faces, edges, angles, and vertices, all of which can be used to represent data. For On-Page SEO Factors, I have found that a tetrahedral shape represents the variables in the most clear and concise way possible (for more on tetrahedrons, please refer to Week 3: Research on Geometry). The three major categories of On-Page SEO would be represented by the base of the tetrahedron, while the pinnacle of of the solid would represent time.

Inputting different data points into this model would then change the tetrahedral shape into a different triangular polyhedron. A perfect tetrahedron would represent the ideal state of a website in terms of search engine success, while any other polyhedron that differs from the Platonic Solid would show what areas need to be improved. By inputting data from different websites into this model, we would essentially create a library of polyhedral shapes. That way if a website owner wants to improve their ranking in search engines, they wouldn’t need to learn a thing about Matrices or Markov Chains. All they would need to do is ensure that the shape of their website either matches the shape of a website they are aspiring to be like or is as close to a perfect tetrahedron as possible. What’s more is that this could also be a fantastic tool for education and training. For example, it could be presented to Marketing students, who would be tasked with creating a successful marketing strategy based on certain variables. The strategies the students have come up with, would then be inputted into the tool and all of the generated shapes would then be compared to each other and to the ideal. This would provide a clear and visual method for training and education, and could be applied to any field that uses some form of variables.

What’s even more exciting is the possibility to make this project a real-time interactive tool through the use of VR. Data Visualisation in VR has not been explored greatly and most efforts thus far have not taken great advantage of the medium. However, I believe this tool would be perfect for VR, because of its immersion and incredible interactive potential. Instead of inputting the data points for this model through a keyboard, one would be able to physically move them and change the data in the Virtual Reality Environment. As one grabs a data point and moves it about, changing its values, the entire shape would change then and there. Placing the model in VR would make the process a lot smoother and faster because moving the data points physically is extremely intuitive and can be much easier than typing different values in. At the end of the experience, the tool would provide concrete numerical data of what needs to be done to achieve the desired shape, allowing users to directly implement the suggested changes.

Concept Pieces

The concept piece below roughly shows how the model may look in the 3D environment. All the different coloured points represent data that could be shifted about to form a different shape, and how the connections between them would change. The larger concept piece represents a top-down view of the model, while the smaller one to the side shows what one of the faces would look like to the side, with its respective data points. The second concept image explains the process of taking the graph into the third dimension and constructing the shapes off of that, thus forming an elaborate library of shapes.


Thoughts and Reflection

Overall, I am very satisfied and excited about this model because of its universality, usefulness and applicability. This is a method for representing any sort of data and can be used as a visual training tool for a multitude of fields. Additionally, it is a great way for the communication of complex data and its intertwining relationships. The tool can be developed and used on computers, tablets, phones, and it could even be a potential breakthrough when it comes to Data Visualisation in VR. The only problem with it so far is that this is very much focused on data and is not really related to games, which can make the model a bit dry for an FMP. Nonetheless, I do believe this is a project worth further research and pursing because of its incredible educational potential, and its value as a piece of clear and concise piece of design.

Week 6: Exploring Ideas and Mechanics by Valzorra

Idea Generation

We have officially entered the Phase 3, the first phase focused on actually building our ideas and creating a variety of prototypes for them. Before, I could start crafting anything, I needed to come up with a sufficient number of potential projects to work on. I already had a few ideas floating around, but this was the perfect time to actually put all of them onto paper and hopefully to come up with a few additional good ones. To do this, I decided to use the Lotus Diagram for Idea Generation, as it maintains ideas rather focused around a broader central concept and the method is also very efficient at forcing me to come up with about 70 concepts. I have attached the Lotus Diagram I came up with below, with the words Chance, Probability, and Maths in the centre.

The diagram itself looks rather intimidating due to the large number of ideas and writing on it, however, after examining everything I had come up with, I decided to focus on a few points that really inspired me. The major idea categories I chose from the centre were to use dice to determine the outcome of a situation and to then change those results, to find a better way for visualising complex data, to use the Reimann-Zeta Function as inspiration for a story, to generate an interactive world through mathematical formulas, and to create advanced and sophisticated AI players could interact with. Below I have attached a series of images featuring the ideas I liked and felt inspired to work on, which have all been highlighted in pink.


After this process of idea generation, I felt quite happy with some of the projects that came to mind and was eager to start working on them as soon as possible. Many of the ideas can be combined, and turned into a more complex and exciting project, which is what I have attempted to do. I will detail each of these in the next couple of weeks in a series of project proposals that will explain my thought process, the connection to my research, and the project itself in a lot more detail. For now, the four major ideas that I would like to dive into are:

  1. A new method for three-dimensional Data Visualisation: I believe I may have figured out a way to represent complex data through the use of three-dimensional solids. This could be used as both an educational and diagnostic tool.

  2. A game environment generated by the players as they move and interact with it it. This would be an exponentially more chaotic experience that would take player actions, feed them into mathematical formulas and functions, and change the environment as they move along. By the end, each player would have created a unique world.

  3. An experience featuring sophisticated AI and based on Edgar Allan Poe’s The Raven. This experience would have predictive and potentially emotive NPCs that would convey a sense of fear in the player, which can be fun and thrilling in itself.

  4. In a world where each individual has one of a set number of special abilities, you play as a character who has managed to figure out how to use all seven of them. You were naturally born with Telekinesis and have infused a standard six-sided dice with the rest. This allows you to control how the dice rolls, giving you power over chance. Additionally, this could incorporate a story loosely based on what may happen if a solution to the Reimann-Zeta function was discovered.

Tech Workshop

We began the Tuesday of Week 6 with an exciting exploration of how Calculus and a bit of Trigonometry can be used in video games to create smooth movement and over the shoulder cameras. I found James’s explanation really straightforward and easy to understand and for the most part I didn’t really have any issues following along. I quite enjoyed this exploration because it showed a very handy practical application of the things we have been looking at over the past few weeks. Additionally, this algorithm and the logic behind it would work equally well in any game engine, because it’s based on mathematics rather than on in-built settings. What’s more is that this is a very elegant mathematical methodology for handling this issue in games design, and I look forward to applying it in some of my future projects. I would be greatly interested in looking and other such applications of Calculus within video games, so hopefully we will be examining more of the sort in the coming weeks. I have attached the notes from that explanation below.


After the lecture on a practical application for Calculus within video games, we entered our Building the World session. James took the time to have one to one sessions with each separate team and to try and help us with our design process. I was one of the first to have a chat with him and as I was interested in developing fun mechanics players can mess around with, James suggested I create a few pieces similar to storyboards, which would describe how those mechanics would work. I decided to start working on a fun idea I had early in this week, which involved a variety of special abilities the player would be able to take advantage of. The complete idea will be described and documented over the course of the next couple of weeks. I also took this opportunity to expand upon the mechanics I was developing last week and to make the illustrations a little nicer and more clear. Additionally, my work from last week (Week 5: Just for Fun) featured a few different abilities in combination with each other, whereas here, I have showcased each one separately.

An environmental sketch to showcase the mechanics onto.

An environmental sketch to showcase the mechanics onto.

The slideshow below described a teleportation mechanics, whereby the player can choose a position within a certain range and be instantly teleported to that location. Another option that may make the mechanic a bit simpler would be to simply teleport the player a set distance in the direction the camera is looking at. This would make the teleportation mechanic less strategic, however, it may simplify things a bit if there is ever a risk of making the game too complex. Additionally, it would be interesting to consider what would happen if a player was to teleport directly on top of an enemy. So far, I believe they will simply not be given the option to do so, but it may be fun if an enemy instantaneously combusts when they are teleported on top of. All food for thought.

A defensive shield would function almost entirely as expected. The player would me a lot less susceptible to damage and enemy projectiles would not necessarily be able to collide with them. I envision the shield as a armour-like material, almost like shards, which would wrap itself around the player and protect them from any danger. The shield would have a relatively long duration and it would last for a certain amount of time. Another option would be to make the shield last onto the player until it is broken by enemies, however, making it based on a timer may be a bit easier to implement and manage.


The last ability I was able work on during our Building the World session was a blinding beam of light that would essentially stun enemies. Initially, I thought that this beam could essentially rise above the ground and shine brightly, blinding enemies with it’s light. The player would be able to pick a target location to place the beam over that location. All enemies within it’s range would be unable to see for a set duration, however, that does not necessarily mean they would not be able to attack. This ability could be a double edged sword as on one side it stuns enemies, but on the other, it definitely draws attention to the player. I may make another version of this in the future as I am not incredibly pleased with it just yet, but nonetheless, so far so good.