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Raining Rainbows design, simplified.
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Time for some easy stitching. I found this free, downloadable embroidery pattern at:
I simplified the design a bit and followed the artist's suggestion to use a product called Sticky Fabri-Solvy to transfer my modified pattern to my fabric. 
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Simplified design on trace paper.
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Using the single sheet feed on my photocopier, I fed in one sheet of the Fabri-Solvy and photocopied my trace paper design. Then I followed the directions on the Fabri-Solvy package - peeled off the backing sheet and stuck the design right down on my blue Essex cloth.  Essex cloth is a linen-cotton blend with a fairly open weave, so it's good for embroidery.  The layer of Fabric-Solvy did make my embroidery needle stick a bit but, for a simple running stitch, sewing through the adhesive sheet and fabric substrate was fine.  
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Light blue Essex cloth and pack of Fabri-Solvy sheets.
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Fabri-Solvy, with design, adhered to cloth and in hoop.
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I initially stitched the cloud outline in white, but decided that would be too low contrast with the blue fabric, so I removed that stitching and resewed with black. Much better. All the stitching done with two plies of DMC embroidery floss, by the way.
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Hard to see white thread on light blue.
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Cloud restitched with black, red rays stitched.
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Continuous stitching started at the eyes, then the mouth and finally the outline.
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All the rays stitched, but yellow and green colors too wimpy.
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I also swapped my original yellow and green threads for richer colors. Once the stitching was complete, I trimmed the excess Fabri-Solvy from the design, following the package instructions. 
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| New green and yellow colors, now finished. | 
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Trimmed and ready to dunk in water.
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Fabri-Solvy flaking off in water.
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 When immersed in warm water (no soap) the adhesive does flake off and dissolve, and I detected no tackiness after the project air-dried. Don't know if I'd use the Fabri-Solvy for something intended as an heirloom, but certainly a convenient way to transfer patterns.  Not sure yet what I will do with my Rainbows - but may simply frame it in a hoop, for display. Stay tuned.