Take after in common usage means that a person resembles an older relative, especially a parent or grandparent. But there is nothing to prevent you from using it as a metaphor, as long as the meaning is clear to your reader. If you feel the relationship between A and B is like the relationship normally conveyed by take after (A is similar to B, an older relative), then by all means write that. For example, you might write that Perl or Java take after C.
Take after has historically been used of people fairly broadly to mean imitation and resemblance:
take, v.
XI. Intransitive uses in idiomatic combination with prepositions.
73. Take after —.
a. To follow the example of; to imitate; hence, to resemble (a parent, ancestor, predecessor, superior, etc.) in nature, character, habits, appearance, or other quality.
1553 T. WILSON Rhet. (1580) 112 If the Nurse be of a noughtie nature, the childe must take thereafter.
1657 HEYLIN Ecclesia Vind. Gen. Pref., His Followers all take after him in this particular.
1678 PHILLIPS (ed. 4) s.v. Imitatives, Patrissare, to take after the Father, or imitate his actions, humor, or fashion.
1892 Gd. Words Nov. 784/2, I take after my mother’s family.
† b. ? To conceive a desire for or inclination to.
1707 Curios. in Husb. & Gard. 6 Men take strangely after this their first Imployment.
References
The Google search [ define take after ] returns a definition and links to various dictionary entries for the phrase.
A New English Dictionary on Historical Principles, Vol. IX, Part II, Su–Th, Sect. T, p. 36ff.