Blue Sphere

Blue Sphere (Japanese: ブルースフィア) is a secret easter egg video game created by attaching Sonic the Hedgehog or Sonic Compilation to the Sonic & Knuckles cartridge. It is a compilation of 134,217,728 Special Stages in the same style and engine of those featured in Sonic the Hedgehog 3 and Sonic & Knuckles. After completing all 227 levels, it repeats from the beginning. In fact, there are actually only 128,016,000 distinct level layouts ("stages" in the game's terminology)—after 128,016,000, the stages repeat, even though the level number continues to advance. After level 134,217,728, however, everything repeats.

These levels are not unique in their design; each level is a 32x32 wrapping square that consists of four 16x16 segments. The layout of each segment is determined from a master list of 128 set layouts (numbered 0 to 127) based on a linear congruence using the level number. If the level number is N, then the top-right segment is (N-1)%128, the bottom-right is (3N-2)%127, the top-left is (5N-3)%126, and the bottom-left is (7N-4)%125, where %n means remainder after division by n. This formula produces the discrepancy between the 227 levels and the 128,016,000 (the least common multiple of 125, 126, 127, and 128) stages.

There is a slight difference between these special stages and those in Sonic the Hedgehog 3 and Sonic & Knuckles; here, the ring counter counts down. If a level is completed with all of the rings collected, the player receives a "perfect" grade and is presented with a screen showing the stage's difficulty level, then advances 10 levels.

The game is accessed from the "No Way! No Way! No Way! No Way?" screen that appears to inform the player that the game that is locked on is not Sonic the Hedgehog 2 or Sonic the Hedgehog 3. Pressing the A, B, and C buttons at the same time changes the screen to the level menu of Blue Sphere and pressing A, B and C on the level menu will switch characters (the player cannot play as Tails, or Sonic and Tails together, as in Sonic 3 &amp; Knuckles).

Blue Sphere can also be created by locking Sonic & Knuckles on to most other Sega Mega Drive/Sega Genesis games, producing one of the levels featured in the Sonic the Hedgehog Blue Sphere, based on information in the game's header (with the games that do not work, simply Sonic & Knuckles will result instead). Beating this level will not take the player to a new one; however, if a perfect score is achieved, a password is displayed. Entering this password into the Sonic the Hedgehog Blue Sphere will skip to that same level, but completing the level will not take the player to the next one either. Note that there are two passwords for each level - one for the ordinary version, from which the player can advance, and one for this version, from which they can not.

It can also be accessed from the file menu's special stage selection in Sonic & Knuckles Collection for PC.

The name Blue Sphere comes from the name shown in its listing in Sonic Mega Collection and Sonic Mega Collection Plus.

Passwords
There are two 12-digit passwords for each level, one for the version from which the player can advance and one for the version from which they can not. There is a simple algorithm for generating both; see http://drspud.no-ip.com/bluesphere/ for a web-based password generator. (The JavaScript/HTML files are available for download for those who want to learn the algorithm.)