Surface-Stable Fractal Dithering is a novel form of dithering invented by Rune Skovbo Johansen for use on surfaces in 3D scenes.

What's unique about it is that the dots in the dither patterns stick to surfaces, and yet the dot sizes and spacing remain approximately constant on the screen, even as surfaces move closer by or further away. This is achieved by dynamically adding or removing dots as needed.

Here's a video explaining how it works:

This repository contains the shader and texture source files, and a Unity example project demonstrating their use. The example project is made with Unity 2019.4 and is also tested in Unity 2022.3.

The core implementation is located in the folder Assets/Dither3D. The remaining files relate to the Unity example project.

The original version of this repository can be found at:
https://github.com/runevision/Dither3D

Each material that uses the dithering has the following dither-specific number properties:

Dither Input Brightness

• Exposure
  Exposure to apply to input brightness (default 1).
• Offset
  Offset to apply to input brightness (default 0).

Dither Settings

• Dot Scale
  Value that exponentially scales the dots.
• Dot Size Variability
  0 = shading controls dot count "Bayer style" (default);
  1 = shading controls dot sizes "half-tone style".
• Dot Contrast
  A value of 1 produces perfect anti-aliasing (default 1).
• Stretch Smoothness
  How much to smooth anisotropic dots (default 1).

Global Options

Furthermore, the following global toggle properties can be set via the Dither3DGlobalProperties component:

• Radial Compensation
  When using a perspective camera, dots must be larger towards the edge of the screen in order to be stable under camera rotation. The Radial Compensation feature can be enabled to achieve this.
• Quantize Layers
  When disabled, dots may grow or shrink in size when they appear or disappear, respectively. Even when enabled, dots may still be partially cut off, but that's a separate and unavoidable effect.
• Debug Fractal
  Displays an overlay effect showing the pattern size, when enabled.

The Dither3DGlobalProperties component can also be used to override the non-global properties of all dither materials at once.

A brief overview of the files in the Assets/Dither3D folder:

The central shader include file with the dithering implementation:

• Dither3DInclude.cginc

Included shader files that use the dithering implementation:

• Dither3DOpaque.shader
• Dither3DCutout.shader
• Dither3DParticleAdd.shader
• Dither3DSkybox.shader

The dither shaders rely on a 3D texture with dither patterns. These come in several versions with different amounts of dots. In the materials using the dither shaders, you can freely switch between these 3D textures.

• Dither3D_1x1.asset
• Dither3D_2x2.asset
• Dither3D_4x4.asset
• Dither3D_8x8.asset

Although the 3D textures are available in the repository, a script is also included which can generate them from scratch. You can do this by using the menu items under the grouping Assets/Create/Dither 3D Texture/....

• Dither3DTextureMaker.cs

The script also generates PNG image files, where the different layers are laid out bottom to top. These PNG files are not used for anything and can be safely deleted, but they are easier to inspect and study than the native 3D textures. Note that later versions of Unity can in principle import 3D textures from such 2D images, but due to an inconsistency between Unity's 3D texture API and their 3D texture importer, the layers will appear in reverse order if this is attempted, and this will cause the fractal dithering effect to not work.

• Dither3D_1x1.png
• Dither3D_2x2.png
• Dither3D_4x4.png
• Dither3D_8x8.png

Here is how I define surface-stable:

• A specific dot "sticks" to the surface whose shading it is part of, both under object movement and camera movement.
• When a pattern is enlarged on the screen, for example due to zooming in on a surface, additional dots may be added to maintain the desired dot density, but no dots may be removed. Likewise, when a pattern shrinks on the screen, dots may be removed, but no dots may be added.

Conforming to the second constraint is in particular what is new in Surface-Stable Fractal Dithering. Approaches that fade between different scales of a pattern, which is not self-similar in the required way, will typically see dots both appearing and disappearing when zooming in.

My implementation conforms to the second constraint by exploiting a certain "fractal" property of Bayer matrices, as explained in the video above.

Some people have suggested using other regular patterns than Bayer for the dithering, based on triangles, hexes, square root 2 ratio rectangles, or similar. This should be relatively straightforward to implement for someone who so desires.

Some people have suggested using blue noise for the pattern. But it is not straightforward to construct a blue noise pattern which is self-similar in a way that conforms to the second surface-stable constraint.

If we use only a single tiled square of blue noise pattern, it would require the dots in each quadrant of the pattern, and each recursive quadrant of the pattern, to perfectly line up with dots in the full pattern, when scaled up to cover the same area as the full pattern.

Some people have pointed to the paper "Recursive Wang Tiles for Real-Time Blue Noise" by Johannes Kopf et al (paper and video). While the paper describes their technique making use of self-similar blue noise patterns, the practical demonstration in the video shows dots fading both in and out while zooming in, so while I do not fully understand their technique in detail, it does not seem to conform to the second surface-stable constraint.

I hope others will manage to construct a tiled blue-noise pattern with the required properties.

This Surface-Stable Fractal Dithering implementation is licensed under the Mozilla Public License, v. 2.0.

You can read a summary here. In short: If you make changes/improvements to this Surface-Stable Fractal Dithering implementation, you must share those for free with the community. But the rest of the source code for your game or application is not subject to this license, so there's nothing preventing you from creating proprietary and commercial games that use this Surface-Stable Fractal Dithering implementation.