rectangular and polar coordinates
xaos flow diagram
Contextually, this refers to the attempted removal of visual artifacts, especially pixel-stepping, from the rendered image.
Flame parameters providing the 'bare bones' characteristics of a given style.
The defining process for creating IFS (and therefore flame) fractals: a random point is 'tranformed' by the mapping function(s) (variations) contained in each of the transforms, the choice of which is influenced by the transform weight. The final fractal, to have sufficient aesthetic appeal, must have been generated by millions of such iterations.
External rendering engine created by Thomas Ludwig.
Pro - fast; smooth unblurred images
Con - limited variation support
Any of the six (three pairs of) numbers required to fully define the basic characteristics of a given transform or post-transform. Essentially, the three number-pairs define the grid positions of each of the triangles' vertices.
Formerly known as 'Color symmetry', this transform-specific parameter controls the distribution of colour around the transform. Appropriate values vary with transform usage, e.g. whether a transform tiles or links from another.
Range -1 to 1.
A variation category characterised by its tendency to constrain the iterations into a limited space.
Formerly dubbed 'Quality', this parameter is directly proportional to the 'hit density' of iterations played out in the Chaos Game. Higher values give a polished, less grainy finish, particularly with blur variations, although the required value should first be estimated by a test render. The range provided in the drop-down box is 200 to 4000, although many artists with powerful computers routinely run at 10x this limit, sometimes as high as 100,000.
A technique implemented in some external rendering engines to dynamically optimise rendering based on hit density. Three new parameters are introduced:
The kernel width (blurring distance) is determined thus:
KernelWidth = Estimator radius / (Density^Estimator curve)
A colouring method not strictly a part of flame fractals that maps the gradient onto the variation's associated coordinate system, usually with variables to fine-tune the appearance. Both the JK and 7X branches support this method, although its implementation is more complete and explicit in the 7X.
Distributed 'living' screensaver project for which Apophysis has provided much source material. Intimately connected with the flam3 rendering engine.
The process of exporting and rendering an Apophysis-created flame in another rendering engine. Each has its unique advantages and drawbacks. Examples include:
Fr0st (as GUI for Flam3/4)
Rendering parameter that sets the level of blur around each pixel. Larger values smooth jagged edges but may result in slight overall blurring. Best determined using post-processing on a test render.
A transform applied to the otherwise-completed fractal, as a whole. The July 2007 revision of 'The Fractal Flame Algorithm' describes it as being "like a non-linear camera".
External rendering engine, a distributed version of which renders for the Electric Sheep.
Pro - a little faster; implements density estimation
Con - limited variation support
External rendering engine based on flam3 but utilising GPU Rendering.
Pro - extremely fast
Con - unfinished; buggy; requires modern graphics card
A file of extension .flame that may contain one or many parameter sets, each of which are commonly, perhaps confusingly, referred to as 'flames'.
An aesthetically-optimised sub-type of IFS originally defined by Scott Draves. These are the type of fractals that Apophysis was created to produce. Essential differences include, but are not limited to, non-linear variations; log-density display; structural colouring; post- and final transforms...
A project created by Vitor Bosshard that morphed from real-time fractal rendering to become a full-fledged flame editor that is essentially Apophysis trimmed and re-packaged for flam3/4 rendering.
A transform, or group of transforms, that produce(s) a structure requiring filling transform(s) to provide more aesthetic appeal. Sometimes the framework may possess some solid structure, others it's esentially 'all hole'.
A rendering parameter that effectively alters the dynamic range of the flame's brightness. Higher values can bring out more detail, but may suppress contrast and introduce grain. Lower values can enhance contrast but may also introduce 'hot-spots'.
Either a) an empty transform or b) a transform whose weight is set to zero (actually 10E-6). To commonsense analysis, such tranforms' influence should be so minimal as to be negligible, thereby implying that deletion would have no visible effect. But sometimes it just does have an effect: thus do ghost transforms establish themselves.
The 256-point colour palette used by Apophysis and stored in a gradient file.
File with .ugr extension that may hold one or many gradients.
A textural artifact of rendering. Sometimes desirable, sometimes the undesirable result of insufficient rendering time.
An area on an image oversaturated with respect to brightness. Occasionally may be desirable in connection with achieving a particular effect, but for the most part to be avoided.
Iterated Function System, the fractal type on which flames are based.
A transform's direct contribution to the flame may be removed by making it invisible, that is setting its opacity to zero.
A single step in the chaos game; or the process thereof.
The pixel-stepping that can ruin the smoothness of a curve.
A transform in a particular intimate relationship with another via xaos, opacity and color speed settings. Essentially, one transform's 'traffic' (hits within the Chaos Game) is routed exclusively through another, which effectively becomes a post-transform with full transform properties. See also:
Whilst a loop can be created by linking a sole transform to another, it is more flexible than that particular relationship. Essentially, two transforms feed each other (and not themselves) via xaos values, the table thus:
xform 1 2 1 0 1 2 1 0
Either, or indeed neither, transform may be invisible. Colour may be introduced by inserting a linked dc_linear transform into the loop. Adding further normal transforms usually requires much xaos and weight adjustment.
Formerly an on/off parameter designated 'transform invisibility', this now takes any value between 0 and 1. Note that it only affects the transform's direct contribution to the picture - even when set to zero, the transform's influence is unaffected.
The factor by which the linear dimension of the fractal is increased before scaling back down in order to provide anti-aliasing. Traditionally, this is accomplished simply by producing the image at higher resolution. In Apophysis, it works differently: the image is artificially inflated by simple replication of the pixels. Because the filter radius is applied before the scale-down, this provides a unique form of anti-aliasing without the burden of rendering at twice the linear dimension. In summary, it uses the same RAM as the traditional method but only a quarter of the rendering time.
A link structure in which one transform is linked to more than one other.
Conceptually, the set of values required to define the flame, in practice represented as an XML structure. For the most part, rendering parameters are saved in default values only.
The point about which transform rotations are performed. Two modes are available:
Local pivot (default) relates to the transform's origin and defaults to (0,0).
World pivot relates to the reference origin, that is the (0,0) of the entire X,Y coordinate system.
Simply a variation not hard-coded into the core software and accessed by placing the corresponding .dll file in the designated folder (plugins or plugins3D, beneath the installation folder.
Effectively a linear transform applied directly after the normal one. All transforms possess one.
The normal method of transform linking: the selected transform's traffic is exclusively routed to that linked.
In Apophysis, this refers to the feature selectable from the render dialogue that allows further manipulation of some key rendering parameters (most notably filter radius and gamma) with minimal time penalty prior to commitment of the final result to a file.
An alternative form of liniking introduced in Apophysis 2.09 beta. The linked transform is introduced before that selected such that its traffic passes exclusively to the selected transform. The implementation, however, is slightly flawed in that it neglects to equalise the weight of linked to that of selected. The same effect may be achieved relatively simply in other versions not supporting pre-linking directly by post-linking then exchanging variations.
Layering as generally understood in the world of digital images is not available within Apophysis. There are, however, various methods available to the more advanced student for at least partially emulating such a feature. Three suggestions to prepare:
1. Duplicate all transforms
2. Duplicate selected transform(s), remembering to halve the weight(s)
3. Link from selected transform(s) then duplicate the link(s)
By default, a fresh install of Apophysis begins with a random batch. Available at any time from the menu or Ctrl-B from the keyboard, there are plenty of options, especially on the Random, Variations and Gradient tabs of Options, to customise this function.
The familiar x,y rectangular coordinates are set as default, but an option to switch to polar (r, θ) is available on the Transform tab of the Editor. Very useful for the more mathematically-minded and for building very structured fractals.
The process of expressing parameters as an image. All screen previews are simply very low-quality renders; creating an image file is "rendering to disc".
Effectively a zoom not linked to hit density. cf. zoom. For full detail, see http://www.ultragnosis.com/fractals/Resources/zoomscale.pdf
A series of instructions to be executed automatically when run. Most commonly, some styles lend themselves to scripting such that random elements may be introduced and a whole set of variations on a theme created at a single hit. Scripts may also be of the strictly utilitarian style such as performing actions on groups of transforms simultaneously. Somewhere between these two types, it is also possible to use a script to create a bare-bones framework ready for further work.
The process of linking more than one transform in series.
A link structure in which multiple transforms link to another.
May be considered as either:
a) a flame fractal designed for the Electic Sheep screensaver
b) the animated loop created therefrom, usually by triangle rotation
A form of grain resembling a faulty spray pattern.
See parallel link.
'Style' is used to denote a particular combination of variations that carries a signature pattern. Often generated from base parameters and sometimes scripts, examples include disc-julians and gnarls.
The technique of variation substitution is all about opening up new pathways from the current flame. The idea is that the initial substitution doesn't in any way change the appearance, but offers potential to change gradually via the variables. Application may be broken down into three specific techniques:
1. Direct substitution.
2. The final transform.
3. Linked transforms.
Prominent examples are the Julia family, wedge-equivalents and linear (e.g. bent2, curve).
A 'quick-and-dirty' render performed at modest dimension and density to determine optimum rendering parameters. Especially useful in conjunction with the post-process feature.
May refer to two techniques:
a) Repetition of motifs using a linear framework of (usually) four or more transforms
b) Creation of a single tile
The mathematical formula, with associated coefficients, that determines the next position of the point in the Chaos Game.
The tangible vehicle for the transform. Their coefficients are simply related: the transform's coefficients are relative to its own origin, whereas the triangle's are relative to the 'world' or reference origin (the 'reference triangle' is the dotted grey triangle remaining when all the others have been cleared/moved).
Parameters of a variation that may be adjusted.
The mathematical formula that transforms the point in the Chaos Game.
The branch-plus-issue number that defines each flavour of Apophysis e.g. 2.09 beta, 7X.14
a) Applied to a transform, this determines the probability that the transform is selected in the Chaos Game via probability of selection = transform weight / Σ(transform weights)
b) Applied to a variation, denotes amount or strength.
The further refinement of transform weight: whereas weight may be seen as a bulk traffic parameter, xaos allows fine-tuning of hit traffic between specific transforms, giving a further dimension of control and enabling hitherto unexplored classes of flames.
Further information: http://www.ultragnosis.com/fractals/Resources/xaos.pdf
A schematic that shows the flow of iteration traffic through the transforms.
A true zoom that automatically compensates for changing density. For use in animations. cf. scale. For full detail, see http://www.ultragnosis.com/fractals/Resources/zoomscale.pdf