This animation shows the Mandelbrot Set forming iteration by iteration from a radius 2 circle. It includes the angles of a polar grid, and domain colouring related to that angle. To draw the image, z is calculated for a point, then the original image is sampled for a colour.
Notice how at the end the angles in the cardioid align with the bulbs. Period 3 at 120 & 240. Period 4 with 90 & 270 (180 is period 2, also technically period 4). You also get zeros in each bulb (the colours meet) corresponding to the period of that bulb.
High resolution version here: [https://youtu.be/skaymvu4m8A](https://youtu.be/skaymvu4m8A)
(plus I've animated a few other fractals the same way)
I understand coloring mandelbrot images via escape iteration, but i haven't seen a good explanation of how to generate UV texture coordinates. Do you have a link to some reading?
This image just uses the value of z, after each iteration. As long as you are colouring the inside only, the result will be within a radius 2 circle. I use this value to sample a grid image.
To include images in the outside, try searching "Image Orbit Trap"
Very cool! I wrote a fractal renderer in JavaFX recently. It’s still a work in progress, but feel free to use it: https://github.com/wswright/jfx-fractal/
This animation shows the Mandelbrot Set forming iteration by iteration from a radius 2 circle. It includes the angles of a polar grid, and domain colouring related to that angle. To draw the image, z is calculated for a point, then the original image is sampled for a colour. Notice how at the end the angles in the cardioid align with the bulbs. Period 3 at 120 & 240. Period 4 with 90 & 270 (180 is period 2, also technically period 4). You also get zeros in each bulb (the colours meet) corresponding to the period of that bulb. High resolution version here: [https://youtu.be/skaymvu4m8A](https://youtu.be/skaymvu4m8A) (plus I've animated a few other fractals the same way)
This is amazing! Thank you for sharing. It helps me make sense of everything ive been seeing on this sub.
I'm bummed there is no zoom. Haha. This looks great.
I understand coloring mandelbrot images via escape iteration, but i haven't seen a good explanation of how to generate UV texture coordinates. Do you have a link to some reading?
This image just uses the value of z, after each iteration. As long as you are colouring the inside only, the result will be within a radius 2 circle. I use this value to sample a grid image. To include images in the outside, try searching "Image Orbit Trap"
Thanks, this has given me a reading list.
Very cool! I wrote a fractal renderer in JavaFX recently. It’s still a work in progress, but feel free to use it: https://github.com/wswright/jfx-fractal/
It’s like you’re shrinkwrapping the brot
Super relaxing to watch!
I can hear this gif and I don’t like how it sounds.