Hello from a rank newbie to here and calculus,
I admire math skills, and I really appreciate how much personal effort is involved maintaining a forum like this. Big thanks!
I found amazing (to me) fractals when an in-memory model of Newton's rings (POVRay raytracer) was rendered to a bitmap (pixelation sampling). But it takes a very long time to process the rendered images and compile to GIF or movie.
I want to build an algorithm on top of the pure math to write a most very fast real-time generator of these moire patterns.
To find the equation for the color of a pixel for any X and Y position on the bitmap, I think Calculus is needed to solve for color = f(x,y) = mystery-integrals.
Here's the 3D problem space:
-A sphere is textured with a pattern of stripes. The orientation of the stripes define an equator and two dots for poles (the hairy ball theorem for stripes).
-An orthographic view (no perspective in the image) of the sphere from the axis of the pole produces an image that 'looks like' Newton's rings.
-Here is an example on my private fiction-wiki... (zero adverts or other images):
https://groupkos.com/dev/images/Newton's_rings_fractal_1000x1000_05054.png
Newton's rings at a pattern-scale of 4.8x10-6 the size of the sphere.
About this image:
There are about 2.4 million rings in the memory-model of the ray-tracer producing the 1000x1000 pixel image. The moire interference is generated by the texturing-algorithm of POVRay when the hyper-fine rings need to be black or gold on the bitmap. The average pixel location has about 2500 stripes of the few million rings in the memory model. What color will 2500 stripes in one pixel be?
Here's the problem space:
Givens:
- The diameter of the sphere the stripes are on,
- the X,Y resolution of the bitmap, and
Variable:
- The scale of the stripe patterns (shrinking the stripe-scale by increments producing a sequence of shrinking stripes).
The solution needed?
What is the color of any one X,Y pixel from a pole view of the striped patterns on a sphere -a binary choice: black or gold?
I do not know enough any more to talk-through the break-down of the problem to an integral. (If you don't use it, ya loose it.)
Is there help for this vanity?
Thank you very much.
-don
P.S. FYI for the moire geek: Moire pattern-acceleration in a radial layout produces a virtual lens effect. The image self-lenses. A lensing of stripes changes the spacing of the stripes, so the lens effect is literally showing a different degree of fractal complexity from a different time-line of the movie. The 'lensing' is an undulation of Newton's rings fractals, appearing as a surface of an illustrated liquid globe.
Perhaps this kind of moire of shrinking-scale can be called stretching-rubber-sheet moire. Does that carry? Hyper-fine-oversampling-pixelation-fractals?
And again, thanks!
I admire math skills, and I really appreciate how much personal effort is involved maintaining a forum like this. Big thanks!
I found amazing (to me) fractals when an in-memory model of Newton's rings (POVRay raytracer) was rendered to a bitmap (pixelation sampling). But it takes a very long time to process the rendered images and compile to GIF or movie.
I want to build an algorithm on top of the pure math to write a most very fast real-time generator of these moire patterns.
To find the equation for the color of a pixel for any X and Y position on the bitmap, I think Calculus is needed to solve for color = f(x,y) = mystery-integrals.
Here's the 3D problem space:
-A sphere is textured with a pattern of stripes. The orientation of the stripes define an equator and two dots for poles (the hairy ball theorem for stripes).
-An orthographic view (no perspective in the image) of the sphere from the axis of the pole produces an image that 'looks like' Newton's rings.
-Here is an example on my private fiction-wiki... (zero adverts or other images):
https://groupkos.com/dev/images/Newton's_rings_fractal_1000x1000_05054.png
Newton's rings at a pattern-scale of 4.8x10-6 the size of the sphere.
About this image:
There are about 2.4 million rings in the memory-model of the ray-tracer producing the 1000x1000 pixel image. The moire interference is generated by the texturing-algorithm of POVRay when the hyper-fine rings need to be black or gold on the bitmap. The average pixel location has about 2500 stripes of the few million rings in the memory model. What color will 2500 stripes in one pixel be?
Here's the problem space:
Givens:
- The diameter of the sphere the stripes are on,
- the X,Y resolution of the bitmap, and
Variable:
- The scale of the stripe patterns (shrinking the stripe-scale by increments producing a sequence of shrinking stripes).
The solution needed?
What is the color of any one X,Y pixel from a pole view of the striped patterns on a sphere -a binary choice: black or gold?
I do not know enough any more to talk-through the break-down of the problem to an integral. (If you don't use it, ya loose it.)
Is there help for this vanity?
Thank you very much.
-don
P.S. FYI for the moire geek: Moire pattern-acceleration in a radial layout produces a virtual lens effect. The image self-lenses. A lensing of stripes changes the spacing of the stripes, so the lens effect is literally showing a different degree of fractal complexity from a different time-line of the movie. The 'lensing' is an undulation of Newton's rings fractals, appearing as a surface of an illustrated liquid globe.
Perhaps this kind of moire of shrinking-scale can be called stretching-rubber-sheet moire. Does that carry? Hyper-fine-oversampling-pixelation-fractals?
And again, thanks!