 Our main concern here, though, is with formulas constructed just using A and the Boolean connectives, and in particular, since we are considering the 1-place case, with such formulas as can be constructed with the aid of these devices and a single sentence letter, p, say. To see how many two-dimensional isotopes a given 1-ary Boolean connective (equivalently, Boolean formula in just one variable) might have, since there are only four such connectives (or formulas), to within equivalence – and for these formulas there is of course no contrast between diagonal and unrestricted equivalence – we should ask how many equivalence classes w.r.t. the relation of unrestricted equivalence there are of the one-variable ‘two-dimensional formulas’ (i.e., here, just Boolean-with-A formulas). This question is easy to answer if we bear the following things in mind: first, that every formula is unrestrictedly equivalent to one in which A occurs, if at all, then just immediately before a sentence letter, and secondly, that w.r.t. the general consequence relation, the formulas p and Ap are completely independent (by contrast with the diagonal consequence relation, w.r.t. which they are equivalent). Thus the (unrestricted) equivalence-classes of one-variable formulas collectively manifest the same Boolean algebraic structure as do the equivalence classes of purely Boolean two-variable formulas. So you can take your favourite Hasse diagram of this 16-element Boolean algebra[55]  and, leaving all occurrences of p intact, replace every occurrence of q with Ap, and you now have a picture of all the two-dimensional one-variable formulas (to within unrestricted equivalence) and the logical relations among them. Each of these 16 equivalence classes (or any of the formulas in such a class) is a two-dimensional isotope of the Boolean equivalence class (or any of its elements) we get by erasing all occurrences of A in the formulas it contains. Thus the two-dimensional formulas p, Ap, and Op most recently encountered, including the first as a degenerate case of a two-dimensional formula for a streamlined account, are two-dimensional isotopes of p, p, and p ↔ p (or ⊤), respectively. You will find that each element of the 4-element Boolean algebra has four distinct elements of the 16-element algebra mapped to it by this erasure-of-A mapping. (This would usually be put by speaking of the principal congruence generated by identifying p’s equivalence class with Ap’s – alias q’s – equivalence class: the smallest congruence relation w.r.t. which these two elements of the algebra are congruent.) For example, p (or its equivalence class) has, to within unrestricted equivalence, the four two-dimensional isotopes p ∧ Ap, the logically strongest isotope w.r.t. general consequence (lowest in the 16-element algebra) and p ∨ Ap, the weakest isotope (highest in the 16-element algebra), and between these two (and mutually incomparable), p and Ap. 