While looking through a used book I bought (Fractals Images of Chaos by Hans Lauwerier) I saw a formula I wasn't familiar with. The formula was discovered in 1969 by French mathematician M. Henon. I entered it into Fracton, played with it a bit, and found a few fractals I liked. Henon is listed in FractInt's built in formula list but I have never seen anyone use it. I have no way to tell if FractInt's Henon is the same as this one.

Here is the par file used to generate the fractal :

Henon_JKO { ; Exported from Fracton.
 reset=2004 type=formula formulafile=fracton.frm
 formulaname=F_20110214_1317 passes=1 float=y
 center-mag=0.32/0.15/0.53333334/1/0/0
 params=-0.0235/0.488/4.6/0/0/0/0/0/0/0
 maxiter=190 inside=190 proximity=0
 colors=000aaateOthNtjNtlMtnMtoLtqLtsKtuKswJswJsvJs\
 uJsuJstJssJssJsrKsqKspKspKsoKsnKsnKsmKslLslLskLsjL\
 siLsiLshLsgLsgMsfMseMseMsdMscMsbMsbMsaNs`Ns`Ns_NsZ\
 NsZNsYNsXNsWOsWOsVOsUOsUOsTOsSOsSOsRPsQPsPPsPPsOPs\
 NPsNPsMPsLQsLQsKQsJQsIQsIQsHQsGQsGRsFRsERsERsDRsCR\
 sBRsBRsASs9Ss9Ss8Ss7Ss7Ss6Ss5Sr4Tq4Tp4To5Tn5Sl6Sk6\
 Sj7Si7Rh8Rf8Re9Rd9QcAQbAQ`BQ_BPZCPYCPWDOWDOWDOWDOW\
 DOWDOVDOVDOVDOVDOVDOUDOUDOUDOUDOUDOTDOTDOTDOTDOTDO\
 TDOSDOSDOSDOSDOSDORCORCORCORCORCOQCOQCOQCOQCOQCOQC\
 OPCOPCOPCPPCPPCPOCPOCPOCPOCPOCPNCPNCPNCPNCPNCPNCPM\
 BPMBPMBPMBPMBPLBPLBPLBPLBPLBPKBPKBPKBPKBPKBPKBPJBP\
 JBPJBPJBPJBPIBPIBPIBPIBPIBPHAQIBQJDQLEQMGQOHQPJQRK\
 QSMQUNQVPQWQQYSQZTQ`VRaWRcYRdZRf`RgaRhcRjdRkfRmgRn\
 iRpjRqlRsnSrnSpnSnnSmnSknSinSgnSfnTdnTbnTanT_nTYnT\
 WnTVnTTnURnUQnUOnUMnUKnUJnUHnUFnVEnVCnVAnV8nV7nV5n\
 V3nV1oW1oW1oW1oW1oW1pV1pV }

frm:F_20110214_1317 {
; Henon's Expression
; From Fractals Images Of Chaos by Hans Lauwerier p126
; x' = y
; y' = -x +2ay + by^2
; Time = 0.4 sec at 640 x 480 with no anti-aliasing
; using Fracton on Mac Pro 2 x 2.8 GHz Quad-Core Xeon
; p1 - Julia constant
; real p2 - bailout
x=real(pixel),y=imag(pixel),
a=2*real(p1),b=imag(p1),bailout=real(p2):
temp=y,
y=a*y+b*y*y-x,
x=temp,
z=x+flip(y),
|z|<=bailout
}