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!
