Shougun is a mysterious person Takumi meets during a chatting session. He sends gore pictures relating to the New Gene incident to Takumi, the equation "fun^10xint^40=Ir2", and the phrase "Whose eyes are those eyes?" which Takumi often used. This event gives Takumi paranoia throughout the story, thinking he is a culprit behind the New Gene incident.
(Source: Wikipedia, Chaos;Head Wiki)