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The White Noise node allows us to generate
completely random values between zero and
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one, based on an input value.
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Just like with the Noise node, the White Noise
node can generate an output based on a one
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to four dimensional input.
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And also like the Noise node, it outputs a
color, composed of three independent noise
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channels, and a value, which carries the same
result as the red color channel.
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But it's different from the Noise node in
that the Noise node has a smoothly varying
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output, meaning that a small change in the
input results in a small change in the output.
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On the other hand, the White Noise node generates
a completely random and independent value
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for each input.
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Given two different inputs, no matter how
close they are two each other, the outputs
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will be completely different.
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However, just like other nodes, when given
exactly the same input, it will generate exactly
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the same output.
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If we feed a texture coordinate into this
Noise, the result is just a gray color.
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This is because for each ray, even within
a single pixel, the texture coordinate will
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be ever so slightly different, resulting in
a completely different noise output.
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And given that for each channel of the noise
the output has an equal probability of being
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any value between zero and one, when the results
of all the rays get averaged for each pixel,
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the result is 0.5 on all channels, which is
a gray color.
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So at the ray level, the colors truly are
all different, but at the pixel level, we
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only see the combined results of several rays.
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This is true for both Cycles and Eevee.
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If we set the render to just one sample, we
can see a completely random color for each
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pixel, as each pixel just gets a single ray,
and nothing gets averaged.
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Note that here I'm zooming into the final
rendered image.
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Zooming with the camera in the viewport has
no effect, and we'll still always see a different
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random color for every single pixel, as each
ray is hitting a different point, no mater
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how close we zoom.
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So the White Noise is useful when we need
to randomize some attribute for each ray.
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But it is also extremely useful when we have
distinct elements that we want to randomize,
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like tiles.
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As long as we have a constant value for each
element, we can feed it into the White Noise,
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and we'll get a different constant output
for each element.
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