Using MobiusN

For a while now, I’ve ocasionally used the MobiusN variation in a final transform to create multiple copies of the fractal and tile them – clearly, the technique is best suited to flames with sharp borders, for example triangles:

L-tiles:

and sierpinski tiles:

With the perfect square of the Sierpinski tile, it dawned on me that I might use different values of the Power variable (other than the obvious 4) with a corresponding distortion of the final transform’s triangle. The brainwave to switch to polar coordinates on the Transform tab really opened up the method – I was soon able to deduce the theta values for the Y and O coordinates based on the Power (n) value as 360/n and 360/n/2 respectively. Thus far, though, I’ve been unable to deduce a formula for the r-value of the O coordinate, resorting to trial-and-error. The following table gives the theta and approximate r values for the O coordinate for 3 <= n <= 12.. Additionally, I've also provided the length l of the XY line of the triangle as I've a hunch this might somehow be involved. Any mathematical geniuses out there who know, or can deduce, the formula for r?

As a bonus, here’s a special effect from using a basic Sierpinski tile with MobiusN final transform with Power = 4, but NOT shifted, so that all 4 copies overlay. As each is at 90 degrees from the its neighbours, the result is a misting of the colours to give an unusual lighting effect.

A look back at 2012

Looking back at 2012, what were my artistic highlights?

It began revisiting a couple of my original styles from 2011, gnarled glynnias and their close cousins I dubbed geologicals

Then I hit on another original combination: the flux-glynnia. Rocky in texture and somehow inherently disturbing, the space offered felt limited, like a single underground cavern system, the abode of pure evil.

A relief, then, to move onto the amazing patterns of linked edisc/julians, looking like some deep Mandelbrot zoom.

Then a brief flirtation with linked splits/elliptic to create spiral forms.

Before the mid-year release of Michael Faber’s e-series plugins, linking back nicely to those edisc/julians.

Then the usual mid-to-late summer doldrums before the final quarter, heavily dominated by Michael Faber’s b-series plugins. Btransform was the variation that I immediately understood, working as a linked pair, the first with power 1 and a split, the second with power ~20, the multiple copies nicely filling the split in the first.

I soon learned to nest them.

Then a similar effect in parallel, using the move variable.

There was also a short spell revisiting gnarls and introducing some original twists: hybrids, hypergnarls and a method for adding texture.

But the b-series called again, this time feeding the entire splits-elliptic pattern through its multiplicative structure.

Beyond the basic gnarl

1. Hybrids

Always on the lookout for a new direction for gnarls, I hit upon the idea of mixing wave variations. They don’t all play well together, but waves2 and auger do. So, starting with basic gnarl parameters, the idea is to keep the total variation weight on transform #2 equal to one. Start with auger 0.1 – 0.2 (and therefore waves2 0.9 – 0.8) and experiment with the auger variables.

2. Hypergnarls

Next level: link the waves transform to an auger transform. Chain-link further if desired.

3. Adding texture

I started this by chain-linking a pulse transform from the auger, but found that it worked just as well introducing about 1% pulse by weight on the original waves transform (that’s pulse = 0.01, other waves variations total = 0.99). The pulse vaiables require crazy values: the scale values divided by, and the frequency values multiplied by, numbers ~10^3.

Need pulse? http://fardareismai.deviantart.com/art/Apophysis-Plugin-Pulse-205212332

Straight hybrid:

Hypergnarled hybrid:

Textured hypergnarl:

A sneaky trick

For variations which possess inner and/or outer variables*, there’s a neat way of changing their areas of influence. As an example, I’ll use the lazyTravis variation. Here’s a basic Sierpinski tile with all 4 linear transforms share-linked to a lazyTravis. I’ve left the variables on default except for introducing lazyTravis_space = 0.08 to more dramatically demonstrate the effect:

To increase the size of the square, reduce the transform size by your chosen value and increase the size of the post-transform by the same. Here, I’ve used 150%:

To reduce the size of the square, simply reverse the above:

And now all 3 in order with the following values introduced:

lazyTravis_spin_in = 0.9
lazyTravis_spin_out = 0.1

Note that these units are pi radians:

*including, but not necessarily limited to:
bSwirl (in conjunction with b-series)
circus
eclipse
eSwirl (in conjunction with e-series)
lazyjess
lazysusan
lazyTravis
loonie (no variables, but similar effect)
ortho
whorl

The ‘b’ series

Well, it’s been a while! Since discovering some posted parameters from Michael Faber, creator of the b-series plugins, a whole new realm had opened up. The parameters consisted of a glynnia transform linked to a bCollide transform which was in turn parallel-linked to a pair of bTransform transforms. The bCollide variables offer scope for experimentation, but the real trick lies with the bTransform variables:

bTransform_rotate
bTransform_power
bTransform_move
bTransform_split

The first bTransform transform should retain the default power value of 1, but a small split value should be introduced (say 0.1 – 0.2). The second bTransform transform should have a much lower weight (say one tenth of that of the first) and a much higher power value (say 20 – 30). This higher power value compresses the transform’s contribution into a narrow strip which, with a little experimentation and adjustment, can be made to fit nicely into the split of the first. And it needen’t stop there – try copying the second bTransform transform and introducing a split in the original. Then raise the power value in this third transform and lower its weight a tad: nested strips, each carrying the overall form as its pattern but in decreasing scale.

With further experimentation, I found that the glynn variation, whilst contributing interesting features, was quite unnecessary for the overall pattern: a linear transform made a perfectly adequate base. Of course, other variations can be used to good effect too. And the bCollide transform may be skipped altogether.

glynnia/bCollide/bTransform

GlynnSim3/bCollide/bTransform

spherical/bCollide/bTransform

ngon+pre-blur/bCollide/bTransform

collideoscope/bTransform

Abort trip

It’s shut up shop! That pile of garbage styling itself as ‘art criticism’ has turned out its final crap and remains only as a dusty museum archive of the tabloid journalism and rag-mag sarcasm spewed forth from the deranged duo that formerly ran it. I only learned the fact today, obliquely, but it’s been gone for over 3 months. I think that calls for a little celebration, so here’s the evil alien troll I’ve adopted as an avatar elsewhere:

TMI #1: new variations

What do you do when a new variation is released? Unzip it into your plugins folder and try it? Of course! Before I get to that stage, however, I generally do some spreadsheet-y things, especially if the variation is one of the small but growing tribe I dub ‘space rearrangers’. I may have more to say in future about these but for the moment, let’s just say that they have a couple of common properties:

1. they possess a variable(s) setting such that they can substitute for linear
2. when applied thus in a Sierpinski tile, they have variable(s) settings such that they can rearrange the tile without introducing any negative space

Most commonly to satisfy #2, this means that the variables must be equalised across all four transforms. Performing this task manually in the editor is a pain, and so I use a method I dub ‘ad hoc scripting’, dropping script snippets into the script editor and running the result. And it’s these snippets that are generated by the spreadsheets. Let’s look at the recently released LazyTravis as an example.

Initially, the new variation is given its own entry on a couple of tabs of a spreadsheet Apo general.xls.

It then gets an entry on the Data tab of scripting.xls to generate its own line in a PowerPro text paste file.

Then the script engine generates the variables for use in ArsClip text pasting.

The final script is generated by:

ArsClip text pasting the loop wrapper
PowerPro text pasting the variations
ArsClip text pasting the variables