User blog:Maxywaxy/Fast growing function i created?

something i made. start at rule 1. If you start with an array [x], step(x) is the value of "step" once the array has been decomposed to [] - a string with nothing in it
 * [Rule 1] Start with an array of positive integers (or zeroes). move to rule 2.
 * [Rule 2] define variable "step" and set it to 1. move to rule 3.
 * [Rule 3] go to the end of the array. move to rule 4.
 * [Rule 4] if the number is a zero, go to rule 5. else, go to rule 6.
 * [Rule 5] remove it and increase "step" by one. move to rule 8.
 * [Rule 6] increase "step" by one. go to rule 7.
 * [Rule 7] decompose the number into "step" copies of the number one less than it. move to rule 8.
 * [Rule 8] go to the new end of the array. move to rule 4.

Decomposing examples: so step(1) is 4. so step(2) is 14.
 * 1
 * 0,0 <- two zeroes because it is step 2.
 * 0
 * 1) (nothing)
 * 2
 * 1,1
 * 1,0,0,0
 * 1,0,0
 * 1,0
 * 1
 * 0,0,0,0,0,0,0
 * 0,0,0,0,0,0
 * 0,0,0,0,0
 * 0,0,0,0
 * 0,0,0
 * 0,0
 * 0
 * 1) (nothing)

the next one is huge: yeah you get it
 * 3
 * 2,2
 * 2,1,1,1
 * 2,1,1,0,0,0,0
 * 2,1,1,0,0,0
 * 2,1,1,0,0
 * 2,1,1,0
 * 2,1,1
 * 2,1,0,0,0,0,0,0,0,0,0
 * 2,1,0,0,0,0,0,0,0,0
 * 2,1,0,0,0,0,0,0,0
 * 2,1,0,0,0,0,0,0
 * 2,1,0,0,0,0,0
 * 2,1,0,0,0,0
 * 2,1,0,0,0
 * 2,1,0,0
 * 2,1,0
 * 2,1
 * 2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
 * 2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
 * 2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
 * 2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
 * 2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
 * 2,0,0,0,0,0,0,0,0,0,0,0,0,0,0
 * 2,0,0,0,0,0,0,0,0,0,0,0,0,0
 * 2,0,0,0,0,0,0,0,0,0,0,0,0
 * 2,0,0,0,0,0,0,0,0,0,0,0
 * 2,0,0,0,0,0,0,0,0,0,0
 * 2,0,0,0,0,0,0,0,0,0
 * 2,0,0,0,0,0,0,0,0
 * 2,0,0,0,0,0,0,0
 * 2,0,0,0,0,0,0
 * 2,0,0,0,0,0
 * 2,0,0,0,0
 * 2,0,0,0
 * 2,0,0
 * 2,0
 * 2
 * 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1

also i computed this, step(3) = 22539988369406

MORE INFO AT Step Copy Function
things

1. growth rate?

2. step(4)?

3. more accurate bounds?