Do the elders appear in a predetermined order?

Solution 1:

According to Alto's Adventure Wikia, there are 5 types of the Elders appearing in game. The Wiki also states that each next elder is a bit faster than the previous one.

The list goes like this:

• The Red Elder. Found at around 2,700m. Chases the player till around 4,000m.
• The Green Elder. Found at around 6,700m. Chases the player till around 8,400m.
• The Yellow Elder. Found at around 10,900m. Chases the player till around 12,600m
• The Blue Elder. Found at around 15,100m. Chases the player till around 17,100m.
• The Black Elder. Found at around 19,600m. Chases the player till around 21,600m.
• The White Elder. Found around 24,100m. Chases the player till around 26,100m

This is where the Wiki stops listing them, but I suppose each consecutive Elder remains the Black one.

Source: Alto's Adventure Wikia - Elders