Workshop 202012 #10


I am not sure what to say artistically about this one. I want to dismiss it, but it holds my attention. It is a mess, but feature that seems “just plain wrong” flip to “compositionally perfect”, and back again.

I like art that challenges me. If you do not, that is ok, thank you for taking a look. Please check the other images, I hope you find something you like that better.

Nerd talk time. Earlier I mentioned “low iteration non-fractals”. I created this to demonstrate why I have been keeping the iteration count low. If the underlying formula is not clean (holomorphic function) the intricate winding spirals that you expect are not there. Instead you get large smoothly colored areas, where the higher iterations add nothing, areas where the fragmentation from the discontinuities dominate, and areas of “dust” with a mix of colors and no defined shape.

Workshop 202012 #6


Low Iteration, Non-Fractal. I started posting these as Workshop because I did not think they fit into a collection. But after posting a few, it is clear that there is a theme here. Someday, I will re-categorize. Too much work today.

As with Workshop 202012 #4 this is bumpy, but continuous, except for tearing along a diagonal in the upper right. It is not a simple rip, there are many fragments. I like the conflict.

Workshop 202012 #5


Yesterday, (Workshop 202012 #4) I got into some nerd talk about exponents of complex numbers. Don’t worry, I am not going there today. Anyway, here is yesterday’s image without the complex exponent. I had decided not to publish this one. It is colorful, but too repetitive, it feels like patterned wallpaper. I pulled it out of the trash bin to compare with yesterday’s picture.

Workshop 202012 #4


Another low-iteration non-fractal.

Warning, nerd talk follows. You may notice a discontinuity running up and right from the center. The underlying formula is this sequence of operations:

z = sin(*sin(\\z = a*z + b\\z = z^{0.9+i*0.1}

z and c have the usual meaning, a and b are parameters. In this case

a = -1.0 + i*1.1\\b=0.0+i*0.1

The first two lines are quite simple. If only the first two lines are used the resulting images are mildly interesting, but also forgettable. If we made the exponent in the third line 1.0, then it is just the identity function z = z, and basically we have just the top two lines.

The exponent in this case is, 0.9+i*0.1, is close to 1.0. It adds a little bit a spice, a little twist to the two-line set.

Complex exponentiation is not, in general, a continuous function. It is a multi-value function. That is an oxymoron since normally a function is defined as something that returns a single value. We define a proper function by picking one of the possible values. There is no way to pick values so that the resulting function is continuous.

So, adding the third line makes the picture more interesting, is also introduces the discontinuity.

Workshop 202012 #3


Many twisting multicolor lines.

I used my fractal program to generate this. It is used in a rather non-fractal way, so do not call this a fractal. (I will skip the tutorial on fractals, please use google if the rest does not make sense.)

The underlying formula is very simple, generally affine transformations with a light sprinkling of the sine function. The number of iterations is kept low, usually single digits or teens. The coloring is not related to Julia set membership or escape-time. The Julia set for this formula is uninteresting, and there are not enough iterations to determine Julia set membership. (Just using fancy mathematical words to say “not a fractal’.)

The low iteration count provides a nice distortion of the basic line or sine wave. Color is based on the current z-value, not the iteration count. Each iteration is colored and overlays the previous.

Workshop 202012 #2


More blended color bands.

I was working on tools or techniques. I draw a single fuzzy wavy line, not as the finished product, but as a prototype to study. How can I vary it? Size, color, waviness. How can this be used alone or with other tools to produce a finished piece?

Inevitably the prototype and experimentation lead to something that I want to finish and publish. Often those get lost because I am in ‘tool’ mode, and do not want to get distracted. They get set aside with the intention to revisit later, and later never comes.

Lately I have made it a policy when I get an interesting prototype to set aside tool development and try to develop a finished piece. Sometimes I can create something that is unique and interesting enough to be worthy of publication. Sometimes it is just a dead end.

To be clear, these are finished pieces, not mere experiments. I may not have started the day with the intention to end up here. Often you cannot plan creativity or inspiration.

Workshop 202012 #1


Starting a new series, “Workshop”. This is catch-all series. Nothing is really planned, there is no particular order. It is best summarized as “what I have been working on lately”

Here I overlay bands of color. The bands are mostly distorted sine waves. They are fuzzy on the edges to blend in with surrounding features.

Someday, I may reclassify these as part of a series. Or maybe not, and this is it, just a bucket of one-off items.