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Fractal T3D

Summary

The Fractal T3D fills the volume with one of three fractals: a quaternion Julia set, the Mandelbulb, or an Iterative fold of a basic shape. Each voxel iterates its own position, so cost grows with Iterations and resolution, and fine detail below a voxel aliases: raise the resolution or Softness rather than expecting detail the grid cannot hold.

Like the shape generators, the fractal is centred on the volume and placed by the transform parameters, and its inside is blended from Background Color to Fill Color at its surface. The fractals give estimated distances, so Softness is a visual control here. The first input sets the resolution and, by default, the fractal is composited over it: see Combining volumes.

Parameters - Fractal Page

Fractal Fractal ⊞ - The fractal to generate. Menu · default Julia

  • Julia Julia - A quaternion Julia set, q → q^Power + C, iterated in four dimensions; the volume shows a 3D slice of it at W-Slice. Voxel positions are divided by 0.35 before iterating.
  • Mandelbulb Mandelbulb - The Mandelbulb, a 3D analogue of the Mandelbrot set in spherical coordinates, 16 iterations. Voxel positions are divided by 0.45 before iterating.
  • Iterative Iterative - An iterated function system: each voxel's position is folded into the positive octant (absolute value) and transformed by each block of Transform, Iterations times, and the distance to Shape is taken from the result. Repeated fold-and-transform builds self-similar structures (Menger-like boxes, sphere clusters).

Aspect Correction Aspectcorrection - Keeps the shape's proportions in voxels when the volume is not a cube: sizes along Y and Z are measured in units of the width, so a sphere stays round (measured: Radius 0.1 in 128 × 64 × 32 is 26 voxels across on every axis). Off, each axis runs from −0.5 to 0.5 across its own extent and the shape stretches with the volume (26 × 12 × 6 voxels). Toggle · default On

Transform Order Xord ⊞ - Order in which scale, rotate and translate are applied to the shape. Menu · default Scale Rotate Translate

  • Scale Rotate Translate srt
  • Scale Translate Rotate str
  • Rotate Scale Translate rst
  • Rotate Translate Scale rts
  • Translate Scale Rotate tsr
  • Translate Rotate Scale trs

Rotate Order Rord ⊞ - Order of the rotations about X, Y and Z. Menu · default Rx Ry Rz

  • Rx Ry Rz xyz
  • Rx Rz Ry xzy
  • Ry Rx Rz yxz
  • Ry Rz Rx yzx
  • Rz Rx Ry zxy
  • Rz Ry Rx zyx

Translate Tx Ty Tz ⊞ - Moves the shape. The volume's centre is 0, and each axis is measured as a fraction of its own extent: 0.5 moves the shape's centre to the face of the volume. Float × 3 · default 0

Rotate R1 R2 R3 ⊞ - Rotation of the shape about each axis, in degrees, around Pivot. Float × 3 · default 0

Scale Sx Sy Sz ⊞ - Scale of the shape along each axis, around Pivot. Float × 3 · default 1

Pivot Px Py Pz ⊞ - Pivot of rotation and scale, measured like Translate. The default 0 is the volume's centre. Float × 3 · default 0

Uniform Scale Scale - Uniform scale, multiplied with Scale per axis. Float · default 1

Fill Color Fillcolorr Fillcolorg Fillcolorb ⊞ - Colour inside the shape. RGBA × 3 · default 1

Fill Alpha Fillalpha - Alpha inside the shape. Float · default 1

Background Color Bgcolorr Bgcolorg Bgcolorb ⊞ - Colour outside the shape. RGBA × 3 · default 0

Background Alpha Bgalpha - Alpha outside the shape. 0 leaves the outside empty, so the shape composites cleanly. Float · default 0

Pre-Multiply RGB by Alpha Premultrgbbyalpha - Not applied in 1.14: the fractal blends Fill Color and Background Color as they are. Multiply the colour by the alpha yourself for premultiplied output. Toggle · default On

Softness Softness - Thickness and softness of the fractal's surface. The fractals give an estimated, not an exact, distance, so this is a visual control rather than a width: larger values thicken fine filaments and blur the edge. In Iterative mode it is multiplied by Iterations, which keeps the look similar as iterations are added. Float · default 0.1 · min 0

Parameters - Julia Page

C C1 C2 C3 C4 ⊞ - The Julia constant, a quaternion (four components). Small changes reshape the set completely; the default −0.72, 0.23, 0, 0 is a connected set. Float × 4 · default -0.72, 0.23, 0, 0

W-Slice Wslice - The fourth coordinate of the 3D slice through the four-dimensional Julia set. Animating it morphs the shape. Float · default 0

Power Juliapower - Exponent of the Julia iteration. 2 is the classic quadratic set. Float · default 2

Parameters - Mandelbulb Page

Phi Shift Phishift - Added to the elevation angle in each iteration, in radians. Twists the bulb's lobes. Float · default 0

Power Mandelpower - Exponent applied to the radius in each Mandelbulb iteration. 8 is the classic Mandelbulb. Float · default 8

P0 P0 - Multiplier of the azimuth angle in each iteration. Equal to Power for the classic Mandelbulb. Float · default 8

P1 P1 - Multiplier of the elevation angle in each iteration. Equal to Power for the classic Mandelbulb. Float · default 8

Parameters - Iterative Page

Shape Shape ⊞ - The shape measured at the end of the folding: a sphere of radius Radius, a cube Radius wide, or a torus of ring radius Radius and tube radius Radius / 2. Menu · default Sphere

  • Sphere Sphere
  • Box Box
  • Torus Torus

Iterations Iterations2 - Fold-and-transform steps. The fractional part blends in one more step, so the parameter animates smoothly. Cost grows linearly with it. Float · default 20

Radius Iterradius - Size of Shape, in the folded space. Float · default 0.4

Transform Transform - The transforms applied in each step, in order. At most three are used. Each is a full transform (order, translate, rotate, scale, uniform scale). The defaults (translate −0.17, rotate 20 / 30 / 40, uniform scale 1.5) give a converging fractal; small changes to them change its character. Sequence · default 0

Transform Order Transform0iterxord ⊞ - Order in which this block's scale, rotate and translate are applied. Menu · default Scale Rotate Translate

  • Scale Rotate Translate srt
  • Scale Translate Rotate str
  • Rotate Scale Translate rst
  • Rotate Translate Scale rts
  • Translate Scale Rotate tsr
  • Translate Rotate Scale trs

Rotate Order Transform0iterrord ⊞ - Order of this block's rotations about X, Y and Z. Menu · default Rx Ry Rz

  • Rx Ry Rz xyz
  • Rx Rz Ry xzy
  • Ry Rx Rz yxz
  • Ry Rz Rx yzx
  • Rz Rx Ry zxy
  • Rz Ry Rx zyx

Translate Transform0itertx Transform0iterty Transform0itertz ⊞ - Translation of this block, in the folded space. Float × 3 · default -0.17

Rotate Transform0iterrx Transform0iterry Transform0iterrz ⊞ - Rotation of this block about each axis, in degrees. Float × 3 · default 20, 30, 40

Scale Transform0itersx Transform0itersy Transform0itersz ⊞ - Scale of this block along each axis. Float × 3 · default 1

Uniform Scale Transform0iterus - Uniform scale of this block, multiplied with its Scale. Float · default 1.5

Parameters - Output Page

Combine with Input Combineinput ⊞ - How the generated volume uses the first input, when one is connected. Menu · default Composite and Set Resolution

  • Set Resolution Only res - The input only sets the output resolution; its content is discarded.
  • Composite and Set Resolution compres - The generated volume is composited with the input using Operation.

Operation Operand ⊞ - Compositing operation between the generated volume and the first input, with the same options as TouchDesigner's Composite TOP. The generated volume is the first operand: with Over, it sits on top of the input. Menu · default Over

Swap Order Swaporder - Swaps the operands of Operation, so the input comes first. Toggle · default Off

Parameters - Common Page

Output Resolution Outputresolution ⊞ - Where the output's width, height and depth come from. With nothing connected to the first input the operator always uses Resolution, whichever option is set. Menu · default Use Input

  • Use Input useinput - The first input's width, height and depth.
  • Custom custom - The Resolution parameter.

Resolution Resolution1 Resolution2 Resolution3 ⊞ - Width, height and depth of the output in voxels. Used when Output Resolution is Custom, or when the first input is not connected. Memory is width × height × depth × bytes per voxel of the Pixel Format: 256³ at 16-bit float RGBA is 128 MiB. Int × 3 · default 64 · min 1

Input Smoothness Inputfiltertype ⊞ - Filtering of the internal GLSL TOPs' input samplers, as TouchDesigner's Input Smoothness. Inputs are read at normalised coordinates, so this matters whenever the input and output resolutions differ or an input is transformed. Nearest Pixel returns voxels unblended; Interpolate Pixels is trilinear. Menu · default Interpolate Pixels

  • Nearest Pixel nearest
  • Interpolate Pixels linear
  • Mipmap Pixels mipmap

Passes Npasses - Has no effect on this operator: its shaders are compute shaders, which read the connected input on every pass, so extra passes repeat identical work. Leave it at 1. Int · default 1

Pixel Format Format ⊞ - Pixel format of the output. Use Input takes the first input's format. With nothing connected, Use Input resolves to 8-bit fixed (RGBA), which clamps values to 0–1 and quantises them to 1/255: set a float format for signed distances, densities above 1, velocities or anything else outside 0–1. Menu · default Use Input

Bypass Bypass - Passes the first input through unchanged and skips the operator's work. With nothing connected the output is a single black voxel. Toggle · default Off

Version Version - T3D version of this operator. Read-only information; include it when reporting a problem. Str

Operator Inputs

  • Input 0: Composite Input T3D_in1 - Optional. Sets the output resolution when Output Resolution is Use Input, and with Combine with Input at Composite the shape is composited with it using Operation.

Operator Outputs

  • Output 0: Output T3D_output - The shape, as colour and alpha.

Performance

GPU time when the operator recooks: 0.093 ms at 64³, 0.104 ms at 128³, all of its passes summed (GeForce RTX 4090, TouchDesigner 2025.33230). An operator whose inputs and parameters are unchanged does not recook and costs nothing.