Image of Four Dimensional Objects

This is written for anyone who is curious about what Four Dimensional Objects look like.

Imagining about Four Dimensional Objects is something hard for most people. Most people think that we live in three dimension world. This common perception is not totally wrong because the universe we live indeed only have three visible spatial dimensions. However we should not forget that there is another non-spatial dimension we are quite familiar with, it is what we usually call time.

By using time as the visualization tool for the fourth dimension, we could represent four dimensional objects as animation of three dimensional objects.

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The image above depicts three super-ellipses that look identical in three dimensions. In fact these super-ellipses have the same time-radius. This time-radius is commonly known as longevity or lifetime. However these super-ellipses have their center located in different position within the time axis.

The central point of the green super-ellipse is located earlier along the time axis, while the red super-ellipse is located in the later part along the time axis.

 

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Super-ellipses having their central point located in the same part of the time axis and different time radius are going to look like the animation above. All these super-ellipses have their central point located in the same part of the time axis. However their time-radius is different is size.

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This particular animation above is harder to explain than the first and the second animation. All the super-ellipses have their central point located in the same part of the time axis and have equal time-radius. However the progress of time affects the change of their three-dimensional appearance differently.

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