Unknown to non-Thinkamancers, (according to LIAB_Text_38) a Thinkagram is not one type of spell. There is a spectrum, from which a Thinkamancer can choose one or more bands to communicate within.
One of the more common forms involves projecting a floating, visual image of the target with Foolamancy before the recipientErf-b1-p109, allowing other Units in the vicinity to observe the effect. Anything spoken by the target is heard by the recipient and other observers. If the two-way version is cast, an image of the recipient is displayed to the target and anyone observing the casting: anything spoken by the recipient is also heard by the target and observers. For the duration of the Spell, the fingers of the Caster are held in a rectangle, index fingers to thumbs of opposite handErf-b1-p068, as a Director or Photographer might in a TV show. The image of the recipient appears in front of this rectangle.Erf-b1-p091
A Thinkamancer can make the Thinkagram more immersive by using Thinkspace, in which the participants communicate in a sort of mental world.
Words need not be spoken aloud during a Thinkagram, and can be mouthed out and mentally projected instead if stealth is necessary.
Prisoners cannot normally receive Thinkagrams, though there are ways to work around this.
A Thinkamancer can either conduct a single long conversation, or several short ones. If a Thinkamancer sends a Thinkagram to another Thinkamancer, the juice cost is halved.
Given the fact that a Thinkamancer can do 1 long conversation or a few short ones, it is likely most of the juice cost is spent initiating it, with a considerably smaller cost needed to maintain it.