It was originally gonna be a hoax, back when SEGA discussed there was a Sonic 3DS game in development, which was revealed as Sonic Generations if I'm correct.
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You guys like concept art, right? The background and setting was inspired by a Sonic artbook.

01. Before it was titled Rush 3D and the debut of the Nintendo 3DS, there was Sonic Rush Frontier. Since the original Rush mostly took place by land, Rush Adventure setting was by sea, it would make sense if the third installment took place by air.

02. Re-arranged the logo alignment and added a jet plane shaped symbol.

03. Last logo concept, made it more slick or streamlined along with two 'fins' corresponding the color scheme of Sonic and Blaze.

04. Since the debut of the new handheld console, the entire logo was completely re-worked and the "Frontier" subtitle was dropped and changed into a simpler and final title: Sonic Rush 3D.
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Wood Grain texture/background made by Hatch1921 from DeviantART. http://hatch1921.deviantart.com/art.....Grain-24243045