ここでのspringは急にとかにわかにという意味で使われているのではないかと思います。

springの動詞の活用欄を参照してください。
http://dic.yahoo.co.jp/dsearch?enc=UTF-8&p=spring&stype=0&dt...

もっとよい表現が浮かぶかもしれませんが、意味合いとしてはこんな感じでしょうか？

飛び出す分解とそれの結合...(concerning the elements in Gala's face).

I feel that the words "apart and together" can be simply expressed as "分解と結合" as in the English without getting into finer details.

I am a great fan of Dali's and have the privilege of seeing a large body of his original works (up really, really close!) in many museums and special exhibitions.

His work does have the 分離/結合 effect as well as other techniques such as his "melting effect."


I used the word 分解 taking the feeling from the below:
分解:
日光をスペクトルに分解する (break apart sunlight into the spectral colors).
飛行機が空中分解した。(The airplane broke apart in midair)

- In the above examples (from the Shogakukan Japanese-English Dictionary), one can almost see the same effect as the elements in Gala’s face breaking apart (分解する).