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 a page with an image:

Here is the par file used to generate the fractal:

Henon_JKO { ; Exported from Fracton.

 reset=2004 type=formula formulafile=fracton.frm

 formulaname=F_20101115_0906 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 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_20101115_0906 {

; 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

x=real(pixel),y=imag(pixel),

a=2*real(p1),b=imag(p1),; p1 - Julia constant

bailout=real(p2),; real p2 - bailout

@beginloop,

temp=y,

y=a*y+b*y*y-x,

x=temp,

z=x+flip(y),

|z|<=bailout

}