Generated with sparks and insights from 3 sources
Based on my analysis of the YouTube video and research into related fractals, the specific fractal demonstrated in the video doesn't have a formal mathematical name. The video shows a procedural technique in Blender that creates a fractal-like pattern using recursive inset and zero-height extrusion operations on cube faces.
What the Video Shows
The YouTube video1 demonstrates a custom fractal generation technique using Blender's Geometry Nodes that involves:
- Recursive Face Extrusion: Each iteration uses the Extrude Mesh node to extrude faces outward by a small offset (0.01 units)
- Scale Element Operations: After each extrusion, the top faces are selected and scaled by a uniform factor (e.g., 0.1)
- Manual Iteration: The process is repeated 4-5 times by duplicating node groups
- Self-Similar Patterns: This creates repeating substructures at progressively smaller scales on each face
Related Mathematical Fractals
While this specific technique lacks a formal name, it shares characteristics with several well-known 3D fractals:
Menger Sponge Family
The closest mathematical analogue is the Menger sponge and its variations. The Menger sponge2 is constructed by:
- Starting with a cube
- Dividing each face into a 3×3 grid (creating 27 smaller cubes)
- Removing the central cube and the central cube on each face (7 total)
- Repeating this process recursively on the remaining 20 cubes
Variations and Related Fractals
The video's approach relates to several fractal variations:
- Jerusalem Cube: Recursively drills Greek cross-shaped holes into a cube2, creating similar face-based recursive patterns
- Mosely Snowflake: A cube-based fractal with corners recursively removed
- mrlysponge Variations: Divide cubes into 5×5×5 or 7×7×7 grids3 and remove central subcubes, with fractal dimensions of approximately 2.73
Mathematical Properties
The technique demonstrated exhibits key fractal characteristics:
- Self-Similarity: Each face undergoes identical extrusion-and-scale operations, producing repeated substructures at smaller scales
- Recursive Structure: The same operation is applied iteratively, creating patterns within patterns
- Scale Invariance: Each iteration reduces the scale uniformly while maintaining geometric similarity
- Finite Iterations: Limited to 4-5 manual iterations, creating a discrete approximation rather than a mathematically infinite fractal
Procedural vs. Mathematical Fractals
What makes this technique distinct is its procedural nature. Rather than implementing a specific mathematical fractal algorithm, it uses:
- General fractal principles (recursion and self-similarity)
- Node-based procedural generation
- Manual iteration control
- Conditional operations based on face area thresholds
The video creator notes that "we don't have any loop node which can actually loop this for the number of iterations so we are going to do some manual work"1, highlighting its procedural rather than algorithmic nature.
Conclusion
While the specific fractal in the video lacks a formal mathematical name, it represents a procedural implementation of recursive face subdivision principles most closely related to the Menger sponge family of fractals. The technique demonstrates how 3D modeling software can be used to explore fractal concepts through iterative geometric operations, creating visually compelling self-similar patterns that share mathematical properties with classical fractals.
Appendix: Supplementary Video Resources
<div class="-md-ext-youtube-widget"> { "title": "Fractals in Blender - Geometry Nodes Extrude Node", "link": "https://www.youtube.com/watch?v=bHWvVtuLJkM&pp=ygUKI2JsZW5kZXI0ZA%3D%3D", "channel": { "name": ""}, "published_date": "Mar 24, 2022", "length": "8:02" }</div>
<div class="-md-ext-youtube-widget"> { "title": "3D Fractals in Blender with Recursive Instancing | Beginner ...", "link": "https://www.youtube.com/watch?v=ZxINVU2YGk0", "channel": { "name": ""}, "published_date": "Dec 17, 2024", "length": "12:30" }</div>
<div class="-md-ext-youtube-widget"> { "title": "This node is just INCREDIBLE - Blender", "link": "https://www.youtube.com/watch?v=nXCSMO4iioA", "channel": { "name": ""}, "published_date": "Jan 9, 2023", "length": "29:04" }</div>
Generated with sparks and insights from 3 sources
Based on my analysis of the YouTube video and research into related fractals, the specific fractal demonstrated in the video doesn't have a formal mathematical name. The video shows a procedural technique in Blender that creates a fractal-like pattern using recursive inset and zero-height extrusion operations on cube faces.
What the Video Shows
The YouTube video1 demonstrates a custom fractal generation technique using Blender's Geometry Nodes that involves:
- Recursive Face Extrusion: Each iteration uses the Extrude Mesh node to extrude faces outward by a small offset (0.01 units)
- Scale Element Operations: After each extrusion, the top faces are selected and scaled by a uniform factor (e.g., 0.1)
- Manual Iteration: The process is repeated 4-5 times by duplicating node groups
- Self-Similar Patterns: This creates repeating substructures at progressively smaller scales on each face
Related Mathematical Fractals
While this specific technique lacks a formal name, it shares characteristics with several well-known 3D fractals:
Menger Sponge Family
The closest mathematical analogue is the Menger sponge and its variations. The Menger sponge2 is constructed by:
- Starting with a cube
- Dividing each face into a 3×3 grid (creating 27 smaller cubes)
- Removing the central cube and the central cube on each face (7 total)
- Repeating this process recursively on the remaining 20 cubes
Variations and Related Fractals
The video's approach relates to several fractal variations:
- Jerusalem Cube: Recursively drills Greek cross-shaped holes into a cube2, creating similar face-based recursive patterns
- Mosely Snowflake: A cube-based fractal with corners recursively removed
- mrlysponge Variations: Divide cubes into 5×5×5 or 7×7×7 grids3 and remove central subcubes, with fractal dimensions of approximately 2.73
Mathematical Properties
The technique demonstrated exhibits key fractal characteristics:
- Self-Similarity: Each face undergoes identical extrusion-and-scale operations, producing repeated substructures at smaller scales
- Recursive Structure: The same operation is applied iteratively, creating patterns within patterns
- Scale Invariance: Each iteration reduces the scale uniformly while maintaining geometric similarity
- Finite Iterations: Limited to 4-5 manual iterations, creating a discrete approximation rather than a mathematically infinite fractal
Procedural vs. Mathematical Fractals
What makes this technique distinct is its procedural nature. Rather than implementing a specific mathematical fractal algorithm, it uses:
- General fractal principles (recursion and self-similarity)
- Node-based procedural generation
- Manual iteration control
- Conditional operations based on face area thresholds
The video creator notes that "we don't have any loop node which can actually loop this for the number of iterations so we are going to do some manual work"1, highlighting its procedural rather than algorithmic nature.
Conclusion
While the specific fractal in the video lacks a formal mathematical name, it represents a procedural implementation of recursive face subdivision principles most closely related to the Menger sponge family of fractals. The technique demonstrates how 3D modeling software can be used to explore fractal concepts through iterative geometric operations, creating visually compelling self-similar patterns that share mathematical properties with classical fractals.
Appendix: Supplementary Video Resources
