Hi Julia community!
This is my first post here, and I’m excited to begin my journey with the Julia programming language. I’m currently working on a personal hobby project focused on visualization. Until now, I’ve been using LaTeX and TikZ, but I’m transitioning to Julia + Makie for better interactivity and flexibility.
The idea came from a simple problem: I didn’t enjoy writing down my dreams in plain text. So, I started representing them visually using a 4×4 matrix, where each transition reflects a symbolic aspect of the dream. I use elements like Aer (air), Aqua (water), and Terra (earth) as symbolic vector nodes. Over time, the concept became more complex — and I realized that my limited math background was holding me back 
My Question
Is there a way to define a space in Julia where each vector has:
- an initial point
- a direction
- a diagonal/orientation
- and a symbolic label (e.g., Aer, Aqua, Terra)?
I’m imagining this as a structured, physics-like vector space, where each object carries both geometric properties and symbolic meaning. If there’s a mathematical framework (algebraic, geometric, group-theoretic…) that could help me formalize this concept, I’d love your guidance.
Additionally:
- How can I track patterns through plots once such a space is defined?
- What’s a good way to store or count these transitions in the matrix for future comparison?
- Would it make sense to create a small package for this system (e.g., with custom types or plotting logic)?
Visual Example
Right now, I use TikZ to create this matrix, but I want to move to Makie for interactive exploration and automated pattern detection:
The gray nodes are key — they represent dream elements or transitions I track. For example:
- falling from air to earth → vector V₁₄
- falling from air to water → vector V₁₂
I know this may be a bit unorthodox, but if you have any feedback — technical or mathematical — I’d truly appreciate it.
Thank you in advance! 
