A look back at 2013

“I see very little now, and very few persons, being almost tired of men and things.”
- John Keats

I have thus far neglected a 2013 retrospective. Time to remedy.

A sparse, then dark, beginning, wrestling with deep personal issues…

Scarface

Scarface

then I banished the clouds by continuous force of will and began playing with rep-tiles

Sacred geometry #1

Sacred geometry #1

Patio planning

Patio planning

before flirting once more with bTransform structures…

Escape from reality

Escape from reality

Miss Match

Miss Match

Higher waska

Higher waska

and then taking aim at the target.

Target selected

Target selected

The way it rolls

The way it rolls

These Roman puzzles

These Roman puzzles

Later on, I developed multi-layered bTransform structures…

The bloom on the harvest

The bloom on the harvest

Higher harmonics

Higher harmonics

Axiomatic

Axiomatic

before revisiting twisted glynnias.

Toltec

Toltec

What will rise

What will rise

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Taking bTransform further

Originally, the bTransform structure first defined by its creator utilised a single transform, itself linked from another, parallel-linked to a pair of bTransform transforms (that looks awfully clumsy, but such is Apophysis’ nomenclature!), the first with bTransform_power set to 1, plus a small bTransform_split value, the second of much lower weight with bTransform_power set to around 20.

Subsequently, I explored extensions to this basic structure:

1. Using a linked series of transforms before the bTransform structure
2. Serial-nesting using diminishing bTransform_split values and increasing bTransform_power values.
3. Parallel-nesting using a larger bTransform_split value in the main transform and utilising the bTransform_move variable in opposing-sign pairs e.g. +0.2, -0.2.

Now I’ve developed a further extension, a new level that may, if desired, be applied beyond any of the above. This is achieved by share-linking the entire bTransform structure to another transform. An example: transforms 1 – 4 are a linked series, transforrms 5 – 7 form a nested bTransform structure. Link a transform from #5; select #6, go to the Xaos tab of the editor, right-click, Clear all then double click “to 8″ (the new linked transform). Repeat for #7 then on the Colors tab, set the opacity for transforms 6 and 7 to zero. You now have the base to work from.

b-layers-1

Optionally build a further linked series or go straight to building another bTransform structure of your choosing.

b-layers-2

Examples of double-layered bTransform structures:

Higher waska

Higher waska

Dreams woven deep

Dreams woven deep

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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:

New beginnings

Choppy seas

L-tiles:

Carpet pile

Patio planning

and sierpinski tiles:

The circus is coming to town!

Gift-wrap

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?

MobiusN table

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 meditative light

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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

Geothermal

A singular geography

Lava flow

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.

That bruised and lunatic mouth

The birthing

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

A stylish bit of tiling

The window seat

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

Upspiraling

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

e-test

Leapfrog

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.

Molecular disorder

Universal transmission

I soon learned to nest them.

Under a strange sky

Conversations with the Self

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

Chain of command

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

That loving feeling

A touch of shimmer

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

The deep-delved roots of being

Those twilight rumours

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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:

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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

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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

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