Don, Welcome to Bill Beaty`s vortex. I have been here about 15 years. Many others have been here since the 1990s.
I look forward to seeing your movie! Thanks for the link to the pdf about the mathematics of basic moire patterns. Would it be correct to say your moire patterns are on the surface of half a sphere? Harry On Sat, Oct 17, 2020 at 11:25 AM Don86326 <don86...@gmail.com> wrote: > Hello VO list, > > > I'm happy to be here. I'm happy to not be expelled for thinking out loud. > [smiley-face emoticon with care-worn wrinkles]. I'm a wannabe scientist, > a.k.a. a child scientist with adult ADD. My hunt for dopamine-producing > personal discoveries brings me to this list -- and wow! Reading the VO > messages for a few months now, I've come to appreciate VO as a place > populated by vocal scientists, and likely a hoard of wannabe-s like me. > This wannabe, though, really is a vortex head. That all may come later. > > But as a child, my child scientist really wanted to see more detail in > moire patterns. Window screens in storm doors when two screens overlap > would produce moire patterns that had a curvature, drawing my attention. > Trying to optimize visual resolution I'd move this way and that, but ever > the detail failed to appear. But now I know that curved interference > patterns in an interference of two rectilinear grids makes no curves, so > the curves I saw were a moire transformation of the non-linearity of the > window screens. Each screen was stretched and mounted in the frame causing > unequal micro-spacing of the screen weave, and the non-linearity of > rectilinearity was produced as a difference-image with less overall > resolution, but encoded with the topology of the interfering medium. > Topology-extraction from moire patterns is now a science affording optical > measurement using only video images and algorithms to exacting degrees. > > About ten years ago, I noticed moire patterns when a texture of stripes on > a sphere in a ray-tracing 3D scene model (that makes photo-realism with > matrix algebra --POVRay.org). My childhood yearn to realize more detail in > window screen moire was right there with me in that frame of mind... (techy > man and child scientist in one skull) "Ah! Let's then increase the > pattern resolution!" I could anticipate the dopamine relief --those > moments when life doesn't seem so incomplete. > > Wow! My child was overwhelmed with what I found! > > In the POVRay ray-tracer, a programmatic representation of an object > adorned by a surface texture in a virtual 3D scene has a 'scaling property' > for the 'surface texture.' By changing that scaling property of surface > stripes in a loop, the stripes on a sphere could be produced as many, many > still-frame images where each image was the same spherical surface, but > with the stripes on the surface shrinking a bit with each frame. It is a > long, long journey watching fractal patterns down to a pattern-scale of ten > to the minus fifteen. > > Humbling: I assume to understand the ray-tracer memory model of hyper-fine > surface stripes is making a threshold-decision per pixel for what to color > each pixel of the rendered-image by how many surface-stripes the > memory-model has in it for that certain image pixel. The authors of POVRay > may be able to help development of a kernel that allows sudden-calculation > of the interference images independently of the POVRay system. If anyone > knows how to help with that computer science, please contact me if your > child scientist wants to play with me. > > It's not a hairy ball, but the theorem applies... stripes on a sphere have > polar dots. A polar view shows latitudinal stripes on a sphere as > concentric circles --with a center dot. When the stripe pattern shrinks, > the dots flash between two colors. [The whole image is only two contrasting > colors.] > > The image linked following is a polar-view of a hyper-fine-striped globe > algorithmically sampled as pixels of an image. The scale of the image is > selected to show a recurrence of the base-interference-pattern <---stripes > seen from a polar view, looking like Newton's rings... > > Image 1) > https://groupkos.com/dev/images/Spherical_moire_giant_stripped_sphere_05054.png > > The scale-ratio of the stripes is 4.8 X 10^(-6) stripes from equator to > pole. (These units are not verified carefully but ballParky.) > > I've been living with these computer-model-generated hyper-interference > images for about a decade now. There are many interesting things going > on. The most obvious at certain hyper-fine interference scale-ratios is a > moire pattern acceleration affect. This is where the interference pattern > will move differently than the base-grid motion. > > Ref: *The Basics of Line **Moiré Patterns and Optical Speedup*: > https://arxiv.org/ftp/physics/papers/0703/0703098.pdf > > I assume (please advise) that it is the *vehicle of pattern-acceleration* > that affords a stunning 'virtual lens' that emerges during the movie. The > 'lens' magnifies the center of the image as the image is round and the > acceleration offset is from radial pattern movement (outer to inner > radius). > > The lens is literally --from the vantage of the surface apparent of the > image-- a lens into the future/past (?) of the animated time-line of > images <---because, the future is a shrunken scale of the same image of > Newton's rings. The self-lensing shrinks itself in places to reveal what > it will look like in future images in those places. > > (?) Does the pattern-expansion occur biased before, after, or before and > after patterns on the time-line of change? > > Would you prefer that I call a wave that modulates the rate-of-change > along a time line --a *timing wave*? Comments? > > > Coming to zero theaters near you soon... > > [A trailer of the movie of the time-line of shrinking hyper-fine > interference of Newton's rings with square pixels goes here] > > This movie is based on twenty-thousand still-frame images of hyper-fine > Newton's rings shrinking in scale [generated w/POVRay last week <--- > copyright generation-code available w/MIT open-source license or such]. > > Spoiler alert! > > In the movie, the tear-drops drip to form new quilt of flashing dots > inside the center ring. The pattern among the dots, on or off, flash > unique patterns <-- and the quilt dot-patterns also predict future > interference patterns to come later in the movie. > > The pulsing bow ties generate dripping tear drops. > > The lens explodes to form an expanding ring. > > The patterns outside the ring slip over the ring fastly, and slow down > inside the ring as a flashing bow tie. > > When the ring explodes, patterns near the outer rim begin to predict > another ring. Later, the predicted outer circumference ring forms and > shrinks in to meet the expanding inner ring, and they collide to dissolve > into a lovely animation of fountains and radiating crowns with a cameo at > center of endless random patterns on a quilt of flashing dots. This begins > a new, slowly changing epoch at a new level of pattern complexity. I.e., > the degree of fractal complexity is quantized between exploding lens events > --epochs of complexity on an exponential slope. The slope is slow with > knees at epochs encapsulating lensing events. > > This exploding-lens effect (like passing through the focus point, or into > a reflecting sphere, as an optical perception) marks an 'event' in a long > long 'epoch' of slow change --while the time-line sequence of still-frames > are observed like a movie of a liquid planet. > > The epochs marked by rapid pattern changes of exploding lenses produce > more complex fractals with each epoch until the complexity is visual > fractal dust. Yet, movies in the dusty regions that were fifteen orders of > magnitude scale difference would organize into an exploding dusty lens, > followed by a dusty ring expanding through noisy texture. > > Here are two more scenes from the coming movie... > > Scale ratio: 4.47 x 10^(-6): The lens has exploded, and is expanding > through the outer fractal patterns. The patterns slip over the ring to > become flashing bow ties that generate dripping tear drops that drop a new > quilt... forming by tear drops at the edges of the quilt. The patterns > flashing on and off of the dots also predict future patterns of complexity > following subsequent 'epochal events' along the calm flashing time line. > > > https://groupkos.com/dev/index.php?title=File:Spherical_moire_giant_stripped_sphere_13240.png > > > Scale ratio: 4.26 X 10^(-6): The ring of the exploding lens has met > another ring traveling from the equator. The two rings merge. The merger > has a rapid delta-T on the edges of the merged band. But in the center of > the band, the 'flat top' presents a magnification of patterns cameo-d > inside the band. The expanding ring by itself has a delta-T at the top of > the ring that moves patterns so fast that the fractal patterns > 'spaghettify' into a perfect circle traveling very fast across the ring in > the time-line of pattern change. > > > https://groupkos.com/dev/index.php?title=File:Spherical_moire_giant_stripped_sphere_18520.png > > This is my first attempt to discuss hyper-fine fractals. Please share > your impressions to allow me to find the 'right speak.' > > > Live long and prosper, > > Lay child out > > > > -- > Stay hydrated! > >
