Today’s post will be short. It’s a follow-up post to my previous Jacob’s Ladder Theory, where in the end I spent most of my time comparing the connections of spheres with depictions of cylinders and cones to get the elusive vectors out of the interconnections of the spheres. This week I learned a couple of more skills in blender and was able to illustrate cones of refraction embedded into almost transparent spheres.
It took a bit of learning, but I finally managed to do it. First, I took a nearly transparent sphere. Then I added into it two symmetrical cones, the length of which side is identical to the radius of the sphere, with the tip touching the center of the sphere and the base encircling the surface of the sphere. When I joined these cones into the sphere, I could make these cone-filled spheres follow the same bending double helix that I’ve worked with these few months. At first, I wasn’t quite sure what the ratio of the radius and height of the cone were, but with just visual checking of how these cones of refraction behaved, I could see that the angle of cone must be 30 degrees. This way the two touching cones form a straight vector from the center of one sphere to the center of the other one. And while I say so myself, this makes for a rather pretty picture
And here is the same image from the side, just for aesthetic purposes:
I’m still not 100 % sure whether I’ll be adding anything mathematical, especially relating to vectors, to the manuscript, but at t least I’ll add the picture to the supplementary information.
I already posted this, but here is an addition to the original post. As soon as I realized that refraction can be visualized with double cones inside spheres, I replaced the small spheres at the centers of dots in my original image of the Jacob's ladder with the double cones. This isn't just visually pleasing. It's a much better illustration of where the vectors come from than anything I've had before.
Let me know, how do you like these images? Like the title says, I call these refractive double cones butterflies, because of their resemblance to them.
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