When Jesus spoke to the woman at the well, as recorded in John 4, He said, "… true worshipers shall worship the Father in spirit and truth; for such people the Father seeks to be His worshipers".
Paul clarifies this in Romans 12 when he writes, "…to present your bodies a living and holy sacrifice, acceptable to God, which is your spiritual service of worship".
He says that worship is presenting yourself as a living sacrifice.
A clean animal, fit for eating and sacrifice, in Leviticus, is described as, "Whatever divides a hoof, thus making split (cloven) hoofs, and chews the cud…".
When we combine Paul's instruction, "to present your bodies as a 'living and holy (set apart) sacrifice' and God's description of the sacrifice, 'cloven hoof and chews the cud', we can surmise that God wants us to be identified by two specific characteristics, which is worship: those who are separate from the world and those who meditate on His Word.
The cloven or split hoof is an illustration of one who has "come out from their midst and be separate," (2 Cor. 6)
It is imperative that the Believer be in the world but not of the world. We are to be separate in our thinking which will result in our being separate (from the world) in our behavior.
Clean animals have several stomachs for the purpose of digestion; they ruminate or chew the cud. The animal will eat grasses and swallow it into the first stomach. It will later regurgitate and once again chew the pre-digested grass. The process continues until the grass is broken down into cellulite which can be digested. It is then passed to a second stomach to continue the process of digestion. Thus, ruminating on grass is taking a large area and eating from it, swallowing and bring it up later to process it further. God specifically uses this animal to depict the process of meditation on the Word. We take large sections, eat (read) from them, then bring them up in our thoughts, ponder (chew) them, swallow, bring them up again in order to digest and benefit from the food.
We see several times in Scripture where the Word is described as food, milk, meat, something to be eaten.
In conclusion, our worship of God, that which is of spirit and truth, is done by offering ourselves to Him as a living and holy sacrifice. It is one who separates himself from the world and who meditates (ruminates) on the Word. This is worship.