Add an animated mask with a linearGradient.
<svg width="596" height="255">
<linearGradient id="prog-mask" x1=0% x2="100%" y1="0%" y2="100%">
<stop offset="0%" stop-color="white" stop-opacity="1" />
<stop offset="5%" stop-color="white" stop-opacity="0">
<animate attributeName="offset" values="0; 1" dur="2s" begin="0s" repeatCount="0" fill="freeze" />
<animate attributeName="stop-opacity" values="0; 1" dur="2s" begin="2s" repeatCount="0" fill="freeze" />
</stop>
<stop offset="100%" stop-color="white" stop-opacity="0" />
</linearGradient>
<mask id="prog-render">
<rect x="0" y="0" width="100%" height="100%" fill="url(#prog-mask)"/>
</mask>
<pattern id="pattern-circles" x="0" y="0" width="20" height="20" patternUnits="userSpaceOnUse">
<circle cx="6" cy="6" r="3" stroke="red" stroke-width="2" fill="transparent">
<animate attributeName="r" values="0; 5" dur="2s" begin="0s" repeatCount="0" fill="freeze" />
</circle>
</pattern>
<!-- The canvas with our applied pattern -->
<rect x="0" y="0" width="100%" height="100%" fill="url(#pattern-circles)" mask="url(#prog-render)"/>
</svg>
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