Sequence Fractals

In mathematics a sequence is an infinite ordered list of numbers. https://en.wikipedia.org/wiki/Sequence

Sequences are cool, I decided to look for ways to combine sequences and fractals.

Of course I can take any topic and wonder how to combine it with fractals so this may not be a brilliant inspiration, rather just the normal inner workings of a fractal addled brain. And actually my short definition of sequence is wrong for multiple reasons. Technically sequences can be infinite or finite and do not have to be numbers. You could have a sequence of turtles. Let's keep it simple and stick with infinite sequences of complex numbers.

Oops, still not quite there. For practical time and space reasons, we won't be using the whole infinite sequence, just the first million or so values.

Today's picture? This is a picture of a particularly messy sequence. The sequence is bounded but does not converge. The picture is a portion of the complex plane with a fuzzy dot for each number in the sequence.

Fractal 198

And another

Fractal 197

Yet another fractal spiral

Fractal 196

At this point I gave up on my software testing and just embraced the fractal creation. The smooth colors are back.

Fractal 195

Another experiment. This time intentionally creating color bands between the fractal arms.

Fractal 194

Another one, In the same neighborhood.

Fractal 193

Same image with monochrome palette.

Fractal 192

This fractal uses iteration count coloring. If you look closely in the big blue areas you can see some color banding.

I was testing software and not in "artist mode". I prefer smooth coloring techniques for fractals, but did not want the where the extra smooth color code getting in the way.

As often happens, I am easily distracted and forgot I was in test mode and wandered off exploring fractal space.

Shattered

I really have no idea what to say about this one. Perhaps it should be titled "Artist Goes Off the Rails"

Spray Splatter Squares 2

Here I added some chaos to the splatter. The splatter is not uniformly random. There are blank spots and clumping and brushing. Interest is generated by screaming "fix me".

Spray Splatter Squares

As before, an experiment that produced a nice piece of abstract art. The idea and technique call for more study and development. Just not this week.

Displaced Lines / Faded Bluejeans

A variation of the previous experiment. It is interesting enough to stand on its own. I think it might work better as a background for something else. Again, that is something that I might look into as some unspecified future date.

Displaced Lines

This one was a test pattern for a distraction that I was letting distract me. Despite the origin I think it makes a nice piece of abstract art.

Fractal Color Experiment

This one is getting close to a "Complexity Limit". The fun decorations around the fractal work well here. But the fractal detail is starting to get lost. When I try this technique with a deeper, more complex fractal, the fractal details become random pixel dust. There are ways to fix that, ways to smooth out the transition from the background to the foreground. I will explore that rabbit hole later.

Fractal Color Experiment

Trying out ways to color the dead space "behind" and escape time fractal. I will probably pursue this further in the future. I was in the middle of something else. So for now, it is a placeholder for a future work.

Cell Structure

Another experiment that led to a singular result. I am pleased with the result, but I do not see how to develop it into a separate series.

Storm Clouds

Another one-off workshop item. I really like this one for some reason. I do not recall my reason or motivation for creating it. In fact I had forgot all about it and rediscovered it when putting together this collection. I just had to finish it and include it here.

Orange Fans

Some of the workshop pieces are one-off. I am experimenting with ideas, and come up with one or two things that are worthy of publishing. Some do not fit into a series. Sometimes the uniqueness is enough, the uniqueness makes them special. Other times I am just not in the mood to pursue the idea further. Sometimes when progress on one idea is slow and discouraging, I step away and create something totally unrelated before I can continue.

I think this one came about from a combination of the above reasons.

Color Synced Fractal

A short palette of five colors is used around a period five point.

I am working on another themed collection. I have a start on it. These things often head off into unexpected directions, and by the time I am done, I regret where I started. So I want to be able to see at least 50% of the collection before publish the first ones.

In the meantime I will publish a random assortment of other things, and call it "Workshop".

Purple-Pink

Here is another shape I came up with for the "coloring book". The simpler version used in the previous images won out. Still this one deserves at least an honorable mention.

I think I am at the end of the "Colors I Hate" series. I was not methodical in picking out the colors. I started out selecting colors at random. Midway through I tried using a color wheel and color theory to select colors. The results were disappointing. Possibly because I was not being careful and not selecting the right colors. It might be interesting to do this with properly and precisely selected colors based on color theory. But not now.