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Description of OptiFine's Custom Animations feature
Based on McPatcher's Custom Animations
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Animated textures
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In Minecraft 1.5, Mojang added the ability to animate any block or item texture (originally a feature provided by MCPatcher). 
However, there is yet no way to animate other textures like mob skins or GUIs. MCPatcher fills the gap enabling 
any rectangular area of any non-block or item texture to be animated. This includes even textures specific to other MCPatcher features 
such as random mob skins or skyboxes.

For block and item textures, including CTM and CIT replacements, continue using Mojang's mcmeta method instead.

To build an animation, first choose a texture and determine the x and y coordinates and width and height of the area you want to animate. 
Create your animation as a vertical strip of frames. The width of the animation should be the same as the width of the area you want to animate. 
The height should be a multiple of the animation area height.

Properties file format

Create a properties file with any name you like. Put it in the assets/minecraft/mcpatcher/anim folder of your texture pack, 
or any subfolder within. Add these properties to the file

  # Custom animation
  from=<path to animation>
  to=<path to texture to animate>
  x=<x coordinate of area to animate>
  y=<y coordinate of area to animate>
  w=<width of area to animate>
  h=<height of area to animate>
  # Optional
  duration=<default frame duration in ticks>
  interpolate=<true|false>
  skip=<interpolation ticks to skip>

See About Properties Files for how to specify paths to texture files (properties_files.txt).

This creates a simple animation that plays each frame in order from top to bottom once for one tick (1/20th second) each and then loops.

Multiple, non-overlapping parts of the same texture can be animated by using the same to value with different from, x, y, w, h values. 
They can even have independent timing and frame order information.

For maximum compatibility, it is best to make x, y, w, and h multiples of 16.

Frame order and timing
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Each custom animation may also specify its animation speed and frame order. In the properties file, add a series of entries

  # Frame timing
  tile.X=Y
  duration.X=Z

X starts at 0 and represents the order you want frames to display in. Y is the tile number in the animation .png file, 
the first tile being 0, the second 1, etc. Z is the duration you want that frame displayed, in game ticks (1 tick = 1/20 second). 
If omitted, duration is assumed to be the default frame duration or 1 if not configured.

For example, suppose your animation file is 16x48 (3 frames). To make it run on a 5-frame cycle with a pause in the middle, 
the properties file might look like this:

  # Animate 5 frames
  tile.0=0
  tile.1=1
  tile.2=2
  duration.2=5
  tile.3=1
  tile.4=0

The animation happens in this order:

  Frame 0: Display animation tile 0 for 1 tick (default duration).
  Frame 1: Display animation tile 1 for 1 tick (default duration).
  Frame 2: Display animation tile 2 for 5 ticks (duration=5).
  Frame 3: Display animation tile 1 for 1 tick (default duration).
  Frame 4: Display animation tile 0 for 1 tick (default duration).
  Go back to frame 0.
  Total: 5 frames over 9 ticks.

References
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https://bitbucket.org/prupe/mcpatcher/wiki/Custom_Animations