Game Dev Engine #14. X-Fractal Recursion.

Channel:

Jason Doucette

Subscribers:

808

Published on November 19, 2023 11:00:05 AM ● Video Link: https://www.youtube.com/watch?v=5-BOHNFkgmU

Game:

Fractal (2010)

Duration: 1:03

605 views

17

2023-11-18. Real-time generation of a recursive fractal, computed on the CPU for the fractals, colors, and 3D transforms: rotation & perspective. No GPU used here except to show the pixels.

DISCOVERY

In the middle of generating a Menger sponge fractal, using a recursive generation, I ended up making this fractal. I cannot find existing work that replicates this, so I believe I've invented a new fractal. I am calling it the "X-Fractal" due to the X pattern that it creates. Also it is fitting for the name Xona -- the name of my video game company, Xona Games, and of his engine that renders it, the Xona System 8.

VICSEK FRACTAL

The closest existing fractals are the Vicsek fractals. In 2D, it matches the same pattern, which is: Take a square, split into 3x3, save the corners and center. (And iterate to infinity with self-replication.) However, its known 3D version -- which is to remove the central cube of the 3x3 split, including the cross; the 6 cubes that share a face (which smells an awful like the Menger sponge to me) -- is not what you see here.

X-FRACTAL

X-Fractal maintains the X pattern on each 3x3 face (of the 3x3x3 cube), and continues the alternate on/off pattern for the remaining inner cube, which is left "on". (Again, recursively iterate to infinity for self-similarity; thus the fractal pattern.) Another creation pattern is merely to alternate on/off patterns for each cube that touches another. That is - no two cubes touch.

COLORING

The 8 origin points have set colors, and proximity to them define the colors of the fractal's individual points. When on an origin point, the color is 100% determined by that point. If in the center (equidistant from all), then it will be mixture of all.

XONA SYSTEM 8

For what it's worth, I'm still designing and implementing the Xona System 8 engine -- which is a game development engine. I'll be creating little graphic demos like this, but it's not really showcasing the engine until I start making games. I'm currently in the middle of the following: Entity Component System, Game Object System, Object Pool System, Animation System.

All of these are tied together quite well, and are the foundation of easy-to-create, behavioural re-use, game sub-systems that allow a basic game to be created from scratch in less than a day. The plan forward is to implement my other retro engines (tile, parallax, road, voxel, shmup, ray cast) sub-engines to live in thin layer above this to allow a sub-24-hour development cycle for a core game prototype to be developed in any of them.

AUDIO

Easy Lemon 60 Second by Kevin MacLeod
Licensed under Creative Commons Attribution 4.0

Playlists:
--------------
- Xona System 8: https://youtube.com/watch?v=PqFQv60p-0E&list=PLjnbT4UISq0YwheLThIhm3LDxIkwpmKeb
- Voxel: https://youtube.com/watch?v=uadGU-stF-w&list=PLjnbT4UISq0bQF1g85tE9jTrKfEtdRYlY
- Ray Cast: https://youtube.com/watch?v=SkaPYZOKPQg&list=PLjnbT4UISq0YcFtRFjFQqK0g6ONNCtrvY
- Graph-All: https://youtube.com/watch?v=kLSc7bZW2Bs&list=PLjnbT4UISq0YLgynFSpLzml4BMC6TDZL2
- Scroll Shmup: https://youtube.com/watch?v=l9bIYkZepPo&list=PLjnbT4UISq0Y_7IAN_zUzxgZnfhXxo_0Q
- Road: https://youtube.com/watch?v=rA4g4VX7ys8&list=PLjnbT4UISq0bnfd1RC3M4PgTgkmhlkikV
- Arena Shmup: https://youtube.com/watch?v=VKjiuq437t0&list=PLjnbT4UISq0adw__Y9B2eXA0LL35TyORU
- Wave Function: https://youtube.com/watch?v=ngctVd9VK8I&list=PLjnbT4UISq0Y8vYnrSauHkBKgOBHXFFdf
- 3D Polygon: https://youtube.com/watch?v=0Qq_euAMP48&list=PLjnbT4UISq0YyjqBGG8Q34Kng5gqDmYrT
- GW-BASIC: https://youtube.com/watch?v=QMQJ7o8e-GI&list=PLjnbT4UISq0bMjb81xFBIWOLhBKFCVkuB

Websites:
---------------
- GitHub: https://github.com/JDoucette
- Blog: http://thefirstpixel.com
- Studio: http://xona.com

Other Statistics