Emergent Patterning 4

I've added two new things to my study of these fascinating structures.

First, I now have several ways to index the sequence.  Up until now, I've been using a spiral pattern from the inside (center of image) outward to an edge that I've defined.  I've added three new options.  First, a spiral pattern from the outside in.  Next, a sequential pattern starting at 0,0 and going to the max dimensions of the image.  Finally, a random sequence.

Second, I'm looking at the sequences generated by the individual objects.  Specifically, the 1st derivative of the sequences is most interesting and usually highly structured.  Higher derivatives don't show much difference from the 1st derivative, so I'll limit my study to those.

Here's the now familiar 'Two Knight' emergent pattern with the sequence in a spiral pattern from the center outward:

Now here's the same 'Two Knight' thing but this time the sequence is a spiral pattern from the outside, inward:

Here is the same 'Two Knight' rule but now the sequence is from the upper right to the lower left, in pixel order:

(ahem, also not so interesting).

Just for completeness, here's the same rules with a random sequence:

take note of the subtle gradient.  I've seen this in all the random sequences I've looked at and can't explain it.

But when I add a third Knight:

I can look at each individual object (color), and I can also see where there's a blank pixel.  Using the inward spiral above, I see this pattern:

And now, let's look at the sequence derivatives.  I'll use this inward spiral as the first (and maybe only) example.

I'll look at the sequence generated by the red object.  To calculate the 1st derivative at each point, I simply subtract the current value from the previous value.  If I plot these differences, I get this:

Here's another example.  This is the 1st derivative plot of the 3rd object (marked in blue) using the linear sequence indexing:

I especially like the patterns made out by the pixels in the sequences that are zero.  Here are a few examples:

Unfortunately, I've yet to find a method to this madness.  So I stab in the dark and explore wherever I land.  I'm surprised by pretty much anything I do.

Emergent Patterning 3

Start off with three 'knights' (that is, objects that can make a move like a knight piece in chess):

and run these through a 1024x1024 spiral and you get:

here's a zoom-in on the center:

Now I add a fourth object that can only move to one space:

and the result is:

again, here's a zoom-in on the center:

I change the 4th object just slightly:

and the result:

and then, as you might expect the next one to be:

next one:

and then finally:

zoomed in a little:

Voyager 2 Jupiter Encounter

This is magnetometer data taken in the days just after the July 1979 encounter with Jupiter.

Made into art:

Emergent Patterning 2

 Here are the five input masks:

... and here is the result:

here's a zoom-in near the center:

Emergent Patterning 1

Five input seeds:

results in the following emergent pattern:

Aphelion 2026 Dawn

Dawn at my location, on the first morning after Aphelion:

Deconstructing Video I

Video is just a sequence of images, so I can deconstruct video in the same way that I deconstruct images.  This way, though, we get a movie instead!

https://www.youtube.com/watch?v=OPm290OeN7c