Japanese language typically does not use spaces, and spelling でんでん(denden) in Hiragana opens the context up to interpretation:
伝 (でん) (den) (life, method, way), could be repeated twice as でん でん (den den).
でんでん could then be a short form of でんでん虫 (でんでんむし) (snail)
かたつむり (蝸牛) (snail)