The following 200 new abelian square-free endomorphisms on 4 letters were found on large grid computations at RAMK.
The programs were firstly written by Veikko Keränen & Kari Tuovinen in 1990 (Lisp & C), and, later, by Viet Pham Hoang &
Veikko Keränen in 2006-2007 (Mathematica & C++). Viet built the grid and organised the runs on it.

Firstly, we present an abelian square-free substitution on 4 letters with 12 words in the image of every letter.

The 12 a2f endomorphisms g making up the substitution (and the 12^4 = 20736 a2f endomorphisms)
have the uniform modulus of 109, and, in every case, the image words g(b), g(c), g(d)
are all obtained by the circular automorphism of {a,b,c,d}* starting from g(a).

The Parikh vectors for each g(a), g(b), g(c), g(d) are the rows of the following matrix:

{{21, 31, 29, 28},
  {28, 21, 31, 29},
  {29, 28, 21, 31},
  {31, 29, 28, 21}}

The 12 image words for g(a):s are as follows, where the dots are added just for readability:

abcacdcbcdcadcdbab.cd.badacdadbdcdbdabdbcbabcbdcb.acd.bdcdadcdbcbabcbdcbcacdcacbadabcbdcbcadbabcbabdbcdbdadbdcbca abcacdcbcdcadcdbab.cd.badacdadbdcdbdabdbcbabcbdcb.adc.bdcdadcdbcbabcbdcbcacdcacbadabcbdcbcadbabcbabdbcdbdadbdcbca abcacdcbcdcadcdbab.cd.badacdadbdcdbdabdbcbabcbdcb.cad.bdcdadcdbcbabcbdcbcacdcacbadabcbdcbcadbabcbabdbcdbdadbdcbca abcacdcbcdcadcdbab.dc.badacdadbdcdbdabdbcbabcbdcb.acd.bdcdadcdbcbabcbdcbcacdcacbadabcbdcbcadbabcbabdbcdbdadbdcbca abcacdcbcdcadcdbab.dc.badacdadbdcdbdabdbcbabcbdcb.adc.bdcdadcdbcbabcbdcbcacdcacbadabcbdcbcadbabcbabdbcdbdadbdcbca abcacdcbcdcadcdbab.dc.badacdadbdcdbdabdbcbabcbdcb.cad.bdcdadcdbcbabcbdcbcacdcacbadabcbdcbcadbabcbabdbcdbdadbdcbca abcacdcbcdcadcdb.ad.bcbadacdadbdcdbdabdbcbabcbdcb.acd.bdcdadcdbcbabcbdcbcacdcacbadabcbdcbcadbabcbabdbcdbdadbdcbca abcacdcbcdcadcdb.ad.bcbadacdadbdcdbdabdbcbabcbdcb.adc.bdcdadcdbcbabcbdcbcacdcacbadabcbdcbcadbabcbabdbcdbdadbdcbca abcacdcbcdcadcdb.ad.bcbadacdadbdcdbdabdbcbabcbdcb.cad.bdcdadcdbcbabcbdcbcacdcacbadabcbdcbcadbabcbabdbcdbdadbdcbca abcacdcbcdcadcdb.da.bcbadacdadbdcdbdabdbcbabcbdcb.acd.bdcdadcdbcbabcbdcbcacdcacbadabcbdcbcadbabcbabdbcdbdadbdcbca abcacdcbcdcadcdb.da.bcbadacdadbdcdbdabdbcbabcbdcb.adc.bdcdadcdbcbabcbdcbcacdcacbadabcbdcbcadbabcbabdbcdbdadbdcbca abcacdcbcdcadcdb.da.bcbadacdadbdcdbdabdbcbabcbdcb.cad.bdcdadcdbcbabcbdcbcacdcacbadabcbdcbcadbabcbabdbcdbdadbdcbca

More a2f endomorphisms over 4 letters:

a2fEndomorphismsOver4Letters_Lengths102-115_200inNumber_EditedForReadability.txt

a2fEndomorphismsOver4Letters_Lengths102-115_200inNumber_WithParikhVectors.txt

You may also copy the image words of the "old"   g85 (from 1990)  and  g98 (from 2002)   as text from below:

© 2003 V. Keränen

Please, copy from the white output cells below:

abcacdcbcdcadcdbdabacabadbabcbdbcbacbcdcacbabdabacadcbcdcacdbcbacbcdcacdcbdcdadbdcbca

bcdbdadcdadbadacabcbdbcbacbcdcacdcbdcdadbdcbcabcbdbadcdadbdacdcbdcdadbdadcadabacadcdb

cdacabadabacbabdbcdcacdcbdcdadbdadcadabacadcdbcdcacbadabacabdadcadabacabadbabcbdbadac

dabdbcbabcbdcbcacdadbdadcadabacabadbabcbdbadacdadbdcbabcbdbcabadbabcbdbcbacbcdcacbabd

abcacdcbcdcadbdcbdbabcbdcacbabdbabcabdadcdadbdcbdbabdbcbacbcdbabdcdbdcacdbcbacbcdcacdcbdcdadbdcbca

dabdbcbabcbdcacbacadabacbdbadacadabdacdcbcdcacbacadacabadbabcadacbcacbdbcabadbabcbdbcbacbcdcacbabd

cdacabadabacbdbadbdcdadbacadcdbdcdacdbcbabcbdbadbdcdbdadcadabdcdbabdbacabdadcadabacabadbabcbdbadac

bcdbdadcdadbacadcacbcdcadbdcbcacbcdbcabadabacadcacbcacdcbdcdacbcadacadbdacdcbdcdadbdadcadabacadcdb

Created by Mathematica  (March 29, 2007)