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Description of IFS Builder 3d scripting language

The program uses IFS scripting language to define attractors (fractals) and 3-dimenstional scene parameters.

General structure of an IFS script file

	camera <camera attributes>;
	light <light source2 attributes>;
	light <light source2 attributes>;
	background(r,g,b,l); // background color/brightness
	<formulas, maps, substitutions>
	set s1 = <structure of the set1>;
	set s2 = <structure of the set2>;
	build <structure of the set3> <material1>;
	build <structure of the set4> <material2>;
First we will give a working script example, and then explain script notations.

Example. The Koch Snowflake

	camera  position (0,0,-80) vertical(0,1,0) fov(50);
	light   color (0,1,0)   position (1, 1,-3) shadows(0);
	light   color (1, 1, 0) position (3,-1,-1) shadows(0);
	background(0,1,1,0.5); // set background color

	s = sqrt(3);
	f1 := translate(1/2, 1/2/s,0) * scale(1/s) * rotate(0,0,-1,150);
	f2 := translate(1,0,0) * scale(1/s) * rotate(0,0,-1,-150);
	f3 := translate(-1/2,s/2,0) * scale(s) * rotate(0,0,-1,30);
	f4 := translate(-1/2,-s/2,0) * scale(s) * rotate(0,0,-1,-90);
	f5 := translate(1,0,0) * scale(s) * rotate(0,0,-1,150);

	set KochCurve = (f1 + f2) KochCurve; // define the Koch curve
	set Snowflake = (f3 + f4 + f5) KochCurve;
	build Snowflake;
The script defines the Koch Curve consisting of two own scaled down copies KochCurve = f1(KochCurve) ∪ f2(KochCurve). Then the Koch Snowflake is defined as the set consisting of three images of the Koch Curve: Snowflake = f3(KochCurve) ∪ f4(KochCurve) ∪ f5(KochCurve).

Note for explanation about difference between the equals '=' sign and ':=' see substitutions section.

Sets and Maps

A Set here is just a set a points in 3d. Under a Map we will understand any transformation of sets in the 3d space into other sets. E.g. map scale(k) contracts all points (x,y,z) into (k*x,k*y,k*z).

Sets in the program are specified by equations like: set S = f1(S) + f2(S) + ... + fn(S); Here S means a set in 3-dimensional space, the plus sign '+' denotes union of sets, and f1,...,fn are affine or Mebius maps in 3D space, each of these is defined as composition of basic maps.

Note that mathematicians use ∪ sign to denote a union of sets, so the correct mathematical notation for the equation above is: S = f1(S) ∪ f2(S) ∪ ... ∪ fn(S). The program uses the plus sign, due to keyboard and character table (ASCII) limititations.

Composion of maps is written with the superposition sign '*'. For example translate(tx,ty,tz) * scale(k) * M means contract the set M by factor k and than translate all its points by vector (tx,ty,tz). Sign of maps superposition can be omitted. Moreover, associativity rule of '+' and '*' operations can be applied, e.g.: f1*(f2+f3)=f1*f2+f1*f3.
Associativity also works with sets, e.g. S=(f1+f2)S is the same as S=f1(S)+f2(S) .

Example of a Map:

	f1 := translate(-1,0,0) * scale(1/2);

Example of a set definition:

	Segment = scale(0.5) * (translate(1,0,0) + translate(-1,0,0)) Segment;

Basic Maps of Sets.

Map nameType*Description
id()S Identical motion.
scale(k)S Contraction to the point of origin with coefficient k.
scale(kx,ky,kz)A Contraction to the point of origin with coefficients kx,ky,kz along according axes.
rotate(x,y,z,angle)S Rotation by the angle around an axis passing through the point of origin and point (x,y,z).
rotate(x,y,z,angle,along,across)A The same rotation as the previous, but additionally with contraction along the axis by coefficient along and in the plane orthogonal to the axis by coefficient across.
rotate(angle)S Rotation by the angle around an axis (0,0,1).
translate(x,y,z)S Translation by vector (x,y,z).
translate(x,y)S Translation by vector (x,y,0).
reflect(x,y,z)S Plane reflection with the plane passing through the point of origin an with normal vector (x,y,z).
matrix(ax,ay,az,bx,by,bz,cx,cy,cz)A Linear transformation by 3x3 matrix:
affine2d(ax,ay,bx,by,tx,ty)A Composition of maps translate(tx,ty,0) * matrix(ax,ay,0,bx,by,0,0,0,0). It's useful to determinate 2-dimensional self-affine fractals.
stretch(x,y,z,k)M Mebius map transforming a ball with unit radius and with the center at the point of origin into the same ball and also transferring the point of origin along vector (x,y,z) by the distance k.
inverse(x,y,z,r)M Inversion with respect to sphere with radius r and center (x,y,z). This Mebius map changes orientation.
bound(x,y,z,r)M It's not actually a map, but operator to label the Set, tha it's bound by a ball with radius r and center (x,y,z). All compositions of Mebius maps which act from this Set to itself must be contractive on the specified ball.
empty()  Map transforming every set into empty set. It's useful to determine random-generated fractals.
section(nx,ny,nz,d)  Intersects a set with the plane given by equation x*nx+y*ny+z*nz=d.
*Note: A - affine map, S - similarity map, M - Mebius map. The program forbids mixing affine maps with Mebius in a same Set definition.


The scene appearance essentially depends on location of the camera (observer). Camera parameters are defined by camera keyword, with following after it camera attributes.

AttributeDefault valueDescription
position(x,y,z)required The point (x,y,z) defines camera (observer) location.
direction(x,y,z)can be calculated automatically Vector (x,y,z) defines direction of the view.
vertical(x,y,z)required Vector (x,y,z) defines vertical direction.
fov(angle)50 degree Number angle defines angle of the field of view in vertical plane.
stereo(eyeDist, scrDist)'mono mode' This attribute turn on 'stereo mode' (two pictures for two eyes) with parameters: eyeDist - distance between eyes, scrDist - distance between viewer and the screen.


The lighting of the scene is calculated by well known ray-tracing algorithm, which requires light sorces and specular properties of surfaces (color, reflectivity, e.t.c.) to be defined.

Note: Color/Brightness in the scripting file can be defined in the form of (r,g,b,lum), where r,g,b is color, and lum is luminescence.
Parameter lum can be omitted, in this case lum=1 will be assumed.

1. Parameters of the scene.

ParameterDefault valueDescription
ambient(r,g,b,lum)(0,0,0,0) Color and brightness of the ambient light.
background(r,g,b,lum)Background color and brightness.
tracing_depth(n)0 Number of consecutive rays reflections. Can be n=0 (no reflections),1,2,3 ...
antialiasing(n)0 Smoothing the pixelization effect. Can be n=0 (turned off),1,2,3 ...
screen_size(width, heght)from UI Set resulting image dimenstion, ignoring the UI settings.
reflect_backgroundoff Turn on reflection of the background in th fractal. The parameter works only while using rays reflections (tracing_depth>1)

2. Light sources.

The following table explains the mining of attributes.

position (x,y,z)RRN/A Point (x,y,z) defines light source location.
direction (dx,dy,dz)N/ARR Vector (x,y,z) defines direction, in which the light source shines.
spot_angles (a1,a2)N/ARN/A angles to define spot size for directional light source.
attenuation (qa,la,ca) by default (1,0,0)N/A Coefficient fo quadratic, linear and constant of source light brightness with re respect to destination.
shadows (1 | 0) by default (1) 1 - source light can be blocked up by objects, 0 - can't be blocked up.
attachment (1 | 0) 1 - source light is attached to object coordinate system, or 0 - to the camera coordinate system.
diffuse (r,g,b,lum) One or more attribute of these shall be defined. Default value is (0,0,0,0) Defines color/brightness of scattered light component of the light source.
specular (r,g,b,lum) Defines color/brightness of reflecting component of the light source.
color (r,g,b,lum) Defines color/brightness of the both scattered light and reflecting component of the light source.
Note: N/A - attribute can't be specified, R - attribute is required.

3. Specular properties of surfaces.

Properties of a surface can be specified just after the build command. Since the build keyword can be specified more then once, it is possible to create objects with different colors and properties of surfaces in one scene.

ambient(r,g,b,lum) Arguments can be given in the form of (r,g,b) or (lum) Defines color/brightness of the ambient color component.
diffuse(r,g,b,lum) Defines color/brightness of the diffuse color component.
specular(r,g,b,lum) Defines color/brightness of the specular color component.
color(r,g,b) for convinience Defines color of the ambient and diffuse components and assigns specular component to (1,1,1).
metall(r,g,b) Defines metallic surface: sets color of the diffuse and specular component.


Substitutions are used to simplify Sets and Maps definition. The general notations is
	<name> := <value>;
It means that all occurences of the <name> in the script below this line will be replaced with the <value>. For example
	sum := a + b;
	result = sum * 3;
is equivalent to
	 result = a + b * 3;

Arithmetical expressions

Arithmetical formulas utilize the same syntax as used in C++/Java/Perl/PHP languages.

Random-generated fractals

When defining IFS (or Digraph-IFS), it's possible to set which maps shoul be selected randomly from given finite set of maps. Here are the rules to define such random-generated IFS:

Control statements

Angles measurement units

angles ( degree | radian ) - sets the angles measurement units, this parameter affects fov, rotate, spot_angles and trigonometrical functions. Default value: degree.


To save an animation frame, save_frame() function is used. To save a sequence of frames, use a repetitive operator.