Harvard GSD | SCI-6338 | Computational Design | Jose Luis Garcia del Castillo Lopez
Harvard GSD | SCI-6338 | Computational Design | Jose Luis Garcia del Castillo Lopez
Academic Project
Academic Project
Harvard GSD | SCI-6338 | Computational Design | Jose Luis Garcia del Castillo Lopez
Academic Project
A 4 dimension journey
A 4 dimension journey
Design an interactive experience that attempts to visualize 4D space through 3D projections
Design an interactive experience that attempts to visualize 4D space through 3D projections
Design an interactive experience that attempts to visualize 4D space through 3D projections
Grasshopper/C#
Rhino
Blender/Python
Javascript
Grasshopper/C#
Rhino
Blender/Python
Javascript
Question
Question
Can we truly comprehend a fourth spatial dimension, or are we forever limited by our three-dimensional perception?
Can we truly comprehend a fourth spatial dimension, or are we forever limited by our three-dimensional perception?
Can we truly comprehend a fourth spatial dimension, or are we forever limited by our three-dimensional perception?
Solution
Solution
Understanding 4D through dimensional analogy
Understanding 4D through dimensional analogy
Understanding 4D through dimensional analogy
The approach treats the fourth dimension as spatial rather than temporal, adding a 'w' axis perpendicular to x,y,z coordinates. By analyzing how 4D objects project into 3D space (just as 3D objects cast 2D shadows), we can develop intuition for fourth-dimensional space through familiar three-dimensional visualization.
The approach treats the fourth dimension as spatial rather than temporal, adding a 'w' axis perpendicular to x,y,z coordinates. By analyzing how 4D objects project into 3D space (just as 3D objects cast 2D shadows), we can develop intuition for fourth-dimensional space through familiar three-dimensional visualization.
What is a higher dimension world?
What is a higher dimension world?
In the movie 'Interstellar', Cooper, was trapped into this bizarre space where the space was always transforming, and he can see all the timelines on earth. So this space is actually a 5 Dimension Space Time. Which means, not like our world have three axes, x,y,z, this space have four axes.
In the movie 'Interstellar', Cooper, was trapped into this bizarre space where the space was always transforming, and he can see all the timelines on earth. So this space is actually a 5 Dimension Space Time. Which means, not like our world have three axes, x,y,z, this space have four axes.
How to visualize 4D objects in a our 3D world?
How to visualize 4D objects in a our 3D world?
The solution compares 4D-to-3D perception with 3D-to-2D projection, making fourth-dimensional space comprehensible through familiar dimensional relationships.
The solution compares 4D-to-3D perception with 3D-to-2D projection, making fourth-dimensional space comprehensible through familiar dimensional relationships.
Process: What will daily objects look like in a 4D world?
Process: What will daily objects look like in a 4D world?
Testing the states of different objects in 3D and 4D space
Testing the states of different objects in 3D and 4D space
Application: What if we replaced 3D objects with mathematical formulas?
Application: What if we replaced 3D objects with mathematical formulas?
From traditional 2D julia sets to various complex, beautiful 4D julia sets
From traditional 2D julia sets to various complex, beautiful 4D julia sets
Visualization: A 2D mathematical formula reveals remarkable visual possibilities in 4D space
Visualization: A 2D mathematical formula reveals remarkable visual possibilities in 4D space
Exploring how simple planar equations transform into complex hypersurfaces, demonstrating the unexpected beauty and complexity when basic mathematical expressions are elevated to higher dimensions.
Exploring how simple planar equations transform into complex hypersurfaces, demonstrating the unexpected beauty and complexity when basic mathematical expressions are elevated to higher dimensions.
Reward
Reward
1st Prize
1st Prize
Best project in 2022 6338_Computational Design
Best project in 2022 6338_Computational Design