Revisiting Ortho/JuliaNs

After more than a year of reworking established combinations and using those discovered by others, I finally stumble upon a variation on an existing pairing worthy of mention. The interaction between the JuliaN family and the circular family of variations is well-known (particularly disc, rings2 and lazysusan), although the combination with ortho is less explored. But a chance encounter set me to looking again – it wasn’t until I employed ngon on the final transform that the real magic began.

Using ngon with sides = 4 but power = 0 rather than the default 2 contains the pattern to the central square instead of spreading it outwards (with power = 2 and sides very large, ngon behaves as spherical). The base pairing of ortho and julian began with variation amounts and triangles at their default unity but with the ortho transform weight increased to 30. Much can be explored by varying the ortho_in parameter and rotating the triangle. The essential innovation began by reducing the ortho variation amount whilst simultaneously increasing the size of the triangle – what happens is that effectively, a ‘frame’ appears, that is the outer portion of the square remains unaffected by the rotation:

framed

Framed

Linking the ortho transform to another (lazysusan in this case) provides further interest:

connections

Connections

golden-age

Golden age

Serial-linking that to whorl (with suitably-adjusted whorl_inside parameter) gives a texture reminiscent of combed oil-paint:

abstract-cat

Abstract cat

peacocks

Peacocks

Switching attention to the ngon final and taking the power negative effectively ‘extrudes’ what was the frame into a ‘tunnel’:

psychedelic-cinema-redux

Psychedelic cinema

And going further:

higher-power

Higher power

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Flux frameworks

I’ve already noted┬áthat a pair of flux transforms can create the so-called ‘gasket’ framework:

Gasket

Gasket

but I’ve never really managed to do much with flux, despite other artists’ affinity for the variation. Until now. The gasket may be reproduced by linking a linear transform to a pair of fluxes (with flux_spread set to -1), one with post-transform rotated 180 degrees. But what about using a different base from linear? Collideoscope (collideoscope_a = 0.5, collideoscope_num = 2) proved interesting, giving a circular pattern of triangles (colour spread is controlled on the fluxes):

Base pattern

Base pattern

Instead of linking the single base transform directly to the fluxes, you can first create a linked chain of, say, 4 transforms before linking the final one to the flux framework:

Generalised setup

Generalised setup

There’s now the option to add further effects using the intermediate transforms, e.g. swirl (via swirl2 or whorl) or wiggle/gnarl (via auger and/or bwraps). Or further rearrange the pattern using the lazies, target, ortho etc.:

Whorl

Whorl

 

Bwraps

Bwraps

 

Target

Target

Further variations may be found by switching geometries: bipolar via bcollide base or elliptic via ecollide base (note that the a variable remains at 0.5 but the num variable should now be set to 1 for these).

Effects may be applied post-framework by share-linking the fluxes to a further linked chain.

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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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