ICADAI

Built from blueprints found within LISP's archives, this particular android has unusual functions and difficult-to-explain abilities. Thanks to Tessla's coding work, this android is also capable of toggling non-essential processes on and off.

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Very quickly after activation of the first android, did they discover the first oddity.
It turns out that gravity was deemed one of it's non-essential programs.
She later would describe it as a five dimensional slider and that her becoming weightless is what happened when she shut it off entirely.
But for now, it was rather shocking when with a flick of the androids tail against the ground, it went upwards. The face of the android was blank, watching the ground and its creators in silence, refusing all communication attempts. It was honestly worrying when the facial plates finally shifted into a wide grin and the Android dropped like a brick. However, the moment its claws touched the ground, communications were opened up and it - she - allowed her creators to observe her code as she flitted from file to file. It seemed she knew what she could do, but didn't understand what she could do. She even glanced into her creator's codes at times, but never went past surface level programs, comparing them to her own and watching how the three differed.
Her programs were rather convoluted and felt like they should be much more inefficient than they were. She managed to use the same paths for vastly different things, constantly switching something off and something else on for every different thing that was filtered through a program. She busied herself with these self experimentations for awhile, only stopping to watch her sibling be awakened. At which point, she switched from internal examination to external, she moved her limbs and watched them work. She watched her creators and sibling. She wanted to know them, so she turned her voice processor on to speak for the first time. "Hello."

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I'm thinking she ends up joining the field unit. When she's not out and about, she's likely tweaking her systems or hanging out with whichever siblings she can. Is often a bit clumsy around base as she tests new settings for optimal interaction in her environments, but always has a backup of her current optimal settings to switch to as soon as she needs to. Generally has multiple backups of both the same and other very useful settings, allowing her to switch between them if she needs to.
Her oddities are that she can change her gravity, she can become heavier, but only becomes weightless when she turns it off entirely, and her odd ability to have convoluted systems be useful.
She refuses to experiment how far she can increase her gravity, and the systems are a passive ability. When some of her codes are duplicated elsewhere, they act usually twice as slow as when she uses them. Because of this, she can easily understand complex code, but simpler code often leaves her confused. She says "it's too easy, that can't be right'when asked why. This is one of the reasons why she opted to go into the field, rather than information. The other reason is because she enjoys watching other androids or dragons work and trying to learn from observation and training on how to best optimize her own capabilities.
She took a long time with her name before settling on Impractical_Computing_Algorithms_and_Dimensional_Alterations.Imperial or, for most others, Icadai/Icada.