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ptrgags β [Animation] 2019-01-20 Hyperdimensional Crossing
#abstract #abstractart #chaotica #fractal #fractalanimation #fractalart #mathart #mobius #complexnumbers
Published: 2019-01-20 16:23:36 +0000 UTC; Views: 280; Favourites: 5; Downloads: 9
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Description
I have to say, this is the first time in my life that I've made something that completely took my own breath away. I dropped everything I was doing and watched the GIF for a good 5 minutes.It's amazing how many neat shapes got packed into this animation, given that the parametric curves I used for this were very simple. Tr a moves on a diagonal line from -2 to 2 + 2i. Tr b moves on a diagonal that goes the other way from 2 to -2 + 2i. The lines intersect on the imaginary axis at 1i, which somehow collapses the image into a horizontal line for a frame.Β
About These Fractals
I've been playing around with the fractal recipes from the book Indra's Pearls by Mumford et al. This set of animations is based on "Grandma's Recipe" given in the book. I use parametric curves to select the two complex number parameters for this recipe with slight changes each frame.
I generated the parameters for this with a Python script I'm working on: (github.com/ptrgags/mobius ), rendered the frames in Chaotica, and combined them into a GIF with ImageMagick.
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Comments: 10
I've got to write another comment,,I think this is exceptional.. maybe do more of them ..!!
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Thank you!! I do plan to make more of these in the future! I've barely scratched the surface of this family of fractals, there's quite literally an infinite number of possible settings to explore! I want to explore more, but I'll have to wait a bit until I have less projects going on.
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Goodness!
I don't know how to make gifs or anything, so I've no clue the amount of effort put into this masterpiece. It's beautiful! Reminds me of bacteria growing and evolving into something new.
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I'm really glad you like it!
This project did take a lot of steps, now that I think about it. Here's a summary of the process if you're interested:
1. Research into this type of fractal. I found a book, Indra's Pearls: The Vision of Felix KleinΒ by Mumford et al. in Drexel's library which talks all about these kinds of fractals. It gave some recipes (one is literally called "Grandma's Recipe" in the book XD). These 5 latest animations were all based on that first recipe, and I've still barely scratched the surface! I'm really busy this term, but there's so much more to explore with this type of fractals in time!
2. Write a ProgramΒ to generate the fractal settings based on the recipe. These animations are 200 frames. Each frame of the animation is a fractal in its own right. Each takes 4 transformations, each with 8 settings to pick. that's 6400 numbers in total! I can't do that by hand XD. So I wrote a Python program that computes all those numbers in such a way that the animation happens smoothly. This is the part that took the longest, it takes time to plan out the code in a way that isn't messy.
3. Play with the Program's Settings. This is the fun part, using the program to design an animation. The explanation of how this works gets rather mathematical, so I'll try to keep it simple. Basically for this "Grandma's Recipe", you give it any two points in the plane, it gives you the settings for one fractal. If I move these points around over time, I get a bunch of different fractals; these are the frames of the animation. So my program lets me specify the path of each point. For example, in this particular fractal animation, the points are moving in straight lines that cross in an X shape. So far, I've been using very simple paths (straight lines, circles), but the results are still awesome!
4. Render the Fractals. My program outputs a .flame file, a file format used by fractal editors Apophysis and Chaotica. In this case, I popped the .flame into Chaotica and set it up to render an image for each of the 200 frames of the animation. Then I wait for an hour or two, this step is simple but takes quite a while to compute a good quality image.
5. Turn frames into a GIF. After the previous step, I now have 200 .png images, one for each frame of the animation. I could have done this in an image editor like the GIMP pretty easily, but I found a different program that makes it easier to automate this step. Now I just have to type one short command and my script does all the work
So yeah, not the typical way to make a GIF, a lot more math-y XD
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Thank you! I'm glad you like it!Β
Got a chance to look at your gallery a bit, albeit with not enough time to comment on much. Really interesting collection of fractals, photography and traditional art! Lots of great works there!
Looking at your work makes me really want to try Incendia someday! I'm only familiar with Apophysis at the moment, though I am itching to try some of the 3D fractal renderers too. Don't think it'll happen soon though, I have a lot of computer graphics projects going on already.
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Good Luck...I'm sure you can do it all x
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All your fractal gifs are amazing! My younger brother was hypnotised by them just like me xD
I would suggest to post them in lower quality tho, they weight a lot and so it takes some time to load them and watch without lags
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Glad you liked them!
Yeah, these GIFs are pretty huge, >30MB each. Let me think, I could always reduce the image resolution to say 400x400 instead of 500x500, and I could also reduce the number of frames (these ones have 200 frames, I could try reducing it to 100). I'll have to play around with it to see what looks good.
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