![]() For more about Segerman's hyperdimensional high jinks, check out Emily Conover's report for ScienceShot and Evelyn Lamb's detailed explanation for Scientific American's Roots of Unity blog (with animated GIF, in 2-D). Visualizing objects in 4-space using computer. There may be info in the training data which taught it such 2d information. You can type in Mandelbrot fractals or Julian fractals, or other 4d shapes like hyper cubes, and see what happens. ![]() I find the 4D Julia shape very interesting and beautiful, so heres how to make it too. While the 2-sphere is embedded in 3-space, 4-dimensional Euclidean space is needed to visualize the 3-sphere. It's just removing noise towards 2d targets. It could be something youve created an illustrator, um, or it. 4D objects in Blender Making fractals in Blender is possible since Blender 3.3. Segerman showed off his sculpture, titled "More Fun Than a Hypercube of Monkeys," this weekend in San Jose, California, at the annual meeting of the American Association for the Advancement of Science. So right now this only works with shapes that have straight edges. But Segerman plays with 3-D projections of the hypercube - and even better, sculptures that show the projections of monkeys hooked up in a hypercube shape. The mathematical objects that live on the sphere in four dimensional space - the hypersphere - are both beautiful and interesting. Because our senses are hard-wired for 3-D at best, there's no way to show a hypercube the way it truly is. Such objects should have eight cubes as "sides" - just as a 3-D cube has six squares as sides, or a 2-D square has four lines as sides. ![]() ![]() One of the simplest 4-D objects is an analog of the 3-D cube, known as a hypercube or tesseract. Similarly, a 4-D object would look like a morphing 3-D shape as it moved through our realm. In Edwin Abbott's book, the two-dimensional denizens of Flatland are flummoxed when a sphere comes to visit: Its 2-D projection looks just like a circle of changing size as it moves through Flatland's permeable plane. ![]()
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