Dear reader I'm not really fond of complex complex functions. They are too complicated for me and I can't follow what they are "doing". So I continued with something much simpler the real valued function f(x)=x^2+c. If you choose c between -2 and .25 then the prisoner set of the orbits of x,f(x), f(f(x),..... is an interval. For c>. 25 all orbits escape and there is no prisoner set. For c<-2 the prisoner set is a Cantorlike set (you can figure these things out by drawing the graph of f(x)=x^2+c for some values of c and then tracing back the orbits of intervals (the prisoner set is invariant not only under forward but also under backward tracing)) So making pictures with f(x,y)=(x^2,y^2)+ (c1,c2) what do you expect? Well choosing c1 and c2>.25 nothing, c1 and c2 between -2 and .25 a rectangular prisoner set. The interesting things are when you choose one or both of c1 and c2 smaller then -2. . If you choose only one of them <-2 then you expect a band-like patron. If both <-2 then you expect a patron with smaller and smaller rectangular parts. Below are some pars. Pictures are indeed as expected. The boogie_woogie pars all have the same value for c1 and c2. But the use of different coloring methods give slightly different but interresting/nice pictures. All the pars renders in seconds, so you don't need to spend much time if you decide to look at them. frm:Jh_square {;Jos Hendriks,2002 if (ismand) z = 0 , c = pixel else z = pixel , c = p1 endif : a=real(z),b=imag(z) z=a*a+flip(b*b)+c real(z)<p2 && imag(z)<p2 } Boogie_Woogie_1 { ; Jos Hendriks ,2002 reset=2000 type=formula formulafile=invest~1.par formulaname=jh_square ismand=n passes=1 center-mag=0/0/0.6666667 params=-2.012450635926158/-2.013287548247079/4/0 float=y colors=000zpC<4>zTBzOBzJB<3>z0AzAM<2>z3az0gz0i<3>z0rz0uz0wz0yz2x<14>ziOz\ kMznJ<3>zzA<3>zoEzlFzjGzgHzeJ<8>zUQzSRzRS<3>zLV<19>zVnzWozWp<5>z`uzavzbw\ <2>zeyzfyzgyzhyziy<3>znyzoyzpy<2>zty<3>zoyznyzmx<3>zgpzfnzelzci<19>zrkzs\ kztl<3>zwlztl<3>zbgzZfzUe<2>zHa<4>zHfzGg<3>zAfz8ez7e<19>zkkzmkzok<3>zwl<\ 4>zndzlbzja<2>zeXzcVzcV<5>zZUzYUzXUzXTzWT<8>zRLzQKzQJ<3>zNFzMEzLD<12>zuC } Boogie_Woogie_2 { ; Jos Hendriks ,2002 reset=2000 type=formula formulafile=invest~1.par formulaname=jh_square ismand=n passes=1 center-mag=0/0/0.6666667 params=-2.012450635926158/-2.013287548247079/4/0 float=y outside=mult colors=000aJB<4>iMEjNFlNF<2>qPHsQIwYB<4>wRBwPBwOB<3>wIBwKBwNBwPB<15>cYGb\ ZG`_H__HZ`HXaI<10>RQOQPOPOPPNPOMQNKR<25>RaERbDRcD<2>ReBSfATdC<10>cIYdG_e\ Ea<3>i5i<12>FBYDCXACW<3>0FS<8>RDWUDXXDX<3>hB_<15>shdtjduld<2>wrexufxuc<3\
uuRuuOtuLsuH<14>GfJEeJBdJ<3>0_K<9>XSK`SKcRK<3>qNL<5>WMWTMXPLZ<3>AKf<3>E\ WdF_dGbc<2>JlaETK991<16>_IA } Boogie_Woogie_3 { ; Jos Hendriks ,2002 reset=2000 type=formula formulafile=invest~1.par formulaname=jh_square ismand=n passes=1 center-mag=-0.00113141/0.401369/9.887676 params=-2.012450635926158/-2.013287548247079/4/0 float=y outside=mult colors=0000jR<2>0eM0cK0cK<5>0ZJ0YJ0XJ0XI0WI<8>0RA0Q90Q8<3>0N40M30L2<6>0d\ 10g10j1<3>0u1<5>0T00O00J0<3>0000AB<2>03R00X00Z<3>00g00j00l00o<3>0Bf0s1<1\ 1>0O80M80J9<3>08C<22>0ad0be0dg<5>0jn0ko0lp<3>0qu<3>0ZR<2>0lQ<6>0Qd0Mf0Jh\ <3>05q<3>0El0Gk0Ij0Lh0NgFPf<9>FlTFnSFpR<3>EzL<3>Sb9WX6_Q2LUC5YM0aW0ef06f\ <5>0_J<3>0s31x01w0<2>0s00r10p10o20m2<16>0RA0PA0OB<3>0ID<2>0PN0RY<9>0k`0m\ `0o`<3>0wa<5>0lS } Boogie_Woogie_4 { ; Jos Hendriks ,2002 reset=2000 type=formula formulafile=invest~1.par formulaname=jh_square ismand=n passes=1 center-mag=0/0/0.6666667 params=-2.012450635926158/-2.013287548247079/4/0 float=y outside=summ colors=0000SA<3>0NC0LD0KD0IE<2>0PO0RZ<9>0ka0ma0oa<3>0wb<4>0nV0lT0jS<2>0e\ N0cL0cL<5>0ZK0YK0XK0XJ0WJ<8>0RB0QA0Q9<3>0N50M40L3<6>0d20g20j2<3>0u2<5>0T\ 10O10J1<3>0000AC<2>03S00Y00_<3>00h00k00m00p<3>0Bg0s2<11>0O90M90JA<3>08D<\ 22>0ae0bf0dh<5>0jo0kp0lq<3>0qv<3>0ZS<2>0lR<6>0Qe0Mg0Ji<3>05r<3>0Em0Gl0Ik\ 0Li0NhFPg<9>FlUFnTFpS<3>EzM<3>SbAWX7_Q3LUD5YN0aX0eg06g<5>0_K<3>0s41x01w0\ <21>0UA } Boogie_Woogie_5 { ; Jos Hendriks ,2002 reset=2000 type=formula formulafile=invest~1.par formulaname=jh_square ismand=n passes=1 center-mag=0/0/0.6666667 params=-2.012450635926158/-2.013287548247079/4/0 float=y outside=atan colors=000SG9<10>iMFjNGlNG<2>qPIsQJwYC<4>wRCwPCwOC<3>wICwKCwNCwPC<15>cYH\ bZH`_I__IZ`IXaJ<10>RQPQPPPOQPNQOMRNKS<25>RaFRbERcE<2>ReCSfBTdD<10>cIZdG`\ eEb<3>i5j<12>FBZDCYACX<3>0FT<8>RDXUDYXDY<3>hB`<15>shetjeule<2>wrfxugxud<\ 3>uuSuuPtuMsuI<14>GfKEeKBdK<3>0_L<9>XSL`SLcRL<3>qNM<5>WMXTMYPL_<3>AKg<3>\ EWeF_eGbd<2>JlbETL992<10>QF8 } Boogie_Woogie_6 { ; Jos Hendriks ,2002 reset=2000 type=formula formulafile=invest~1.par formulaname=jh_square ismand=n passes=1 center-mag=0.00500626/-0.0250417/4.901961 params=-2.012450635926158/-2.013287548247079/4/0 float=y outside=atan colors=000ISEDSD9RC<3>5P84P73O6<2>0L3<6>Xd2ag2ej2<3>xu2<5>VT1PO1KJ1<3>00\ 0AAC<2>J3SM0YN0_<3>T0hV0kW0mY0p<2>`8iaBg`Cg<17>DXjCYkBZk<3>5cl<17>QGnSFn\ TEnUCnVBnX9o<24>LENLEMKFL<2>JFIIGGKHG<4>ZOGaPGdRG<3>pXGnXJPmn<3>DgfBfdAe\ b8c_<19>mraosartb<3>zwbwtb<3>ibYeZXbUW<2>SHS<3>bHWeHXhGY<3>rAXt8Wv7W<19>\ xkaymayoa<3>ywb<4>tnVtlTsjS<2>peNocLncL<4>i_KgZKfYK<3>bVJ<3>MTF } Boogie_Woogie_7 { ; Jos Hendriks ,2002 reset=2000 type=formula formulafile=alle.frm formulaname=Jh_square ismand=n passes=1 center-mag=0/0/0.6666667 params=-2.012450635926158/-2.013287548247079/4/0 float=y outside=imag colors=000<8>000000000<3>000zzz<88>zzz<4>zzzccc<143>ccc } Beach_Tent_Stuff { ; Jos Hendriks ,2002 reset=2000 type=formula formulafile=alle.frm formulaname=Jh_square ismand=n passes=1 center-mag=-1.12092/0.549035/5.495472 params=-2.074165287254229/-0.1060234799935393/4/0 float=y maxiter=30 colors=@goodega.map } More_Stuff { ; Jos Hendriks ,2002 reset=2000 type=formula formulafile=alle.frm formulaname=Jh_square ismand=n passes=1 center-mag=0/0/0.6666667 params=-1.266704348177156/-2.115420862728206/4/0 float=y maxiter=30 colors=000Pmm<3>DgeBfcAea8cZ<19>mr`os`rta<3>zwawta<3>ibXeZWbUV<2>SHR<3>b\ HVeHWhGX<3>rAWt8Vv7V<19>xk`ym`yo`<3>ywa<4>tnUtlSsjR<2>peMocKncK<4>i_JgZJ\ fYJ<3>bVI<3>MTEISDDSC9RB<3>5P74P63O5<2>0L2<6>Xd1ag1ej1<3>xu1<5>VT0PO0KJ0\ <3>000AAB<2>J3RM0XN0Z<3>T0gV0jW0lY0o<2>`8haBf`Cf<17>DXiCYjBZj<3>5ck<17>Q\
GmSFmTEmUCmVBmX9n<24>LEMLELKFK<2>JFHIGFKHF<4>ZOFaPFdRF<3>pXFnXI }