I don't know a more correct name for the polynomial type mandeloids which have two power terms, such as the ones Jim Muth has lately been using for his FOTDs, so use that term to refer to them. As we know, the inside of such sets will not be completely rendered by starting the iteration sequences on a single critical point, and they always have at least two critical points. Possibly a subset of the critical points will generate the complete inside set; but the problem I've recently encountered doesn't seem to relate to that, because in each case I rendered the set with (I think) all critical points. It may be a result of my making a mistake in the formula, or maybe it is an artifact of calculation; the problems do not appear with bimandeloids with integer powers, nor usually with fractional power ones, but in the following cases the behavior is strange: in the first case a straight linear border of the inside set along a substantial portion of the negative x-axis, and in the second case suspicious horizontal lines rendered as if they were part of the inside set (color 0). These things don't seem likely to be in the actual fractals, so if anyone has seen these effects before and knows what causes them, or sees errors in my formula, please enlighten me. Regards, Hiram ===================BEGIN PARS========================= BimandWithKEq-1i { ; z->z^5+(0-1i)*z^3.5+C ; Is the "fault line" on the negative real axis genuine? ; Fractint Version 2003 Patchlevel 1 reset=2003 type=formula formulafile=exprmntl.frm formulaname=Bimandeloid passes=1 center-mag=-0.112597/0.0884386/0.8509822 params=5/3.5/0/-1/400/4 float=y maxiter=1000 inside=0; colors=@spectrum.map colors=000zzzc00<7>o00p00r00s00u00w00<9>lIBjJCiLD<3>dTI<4>nTApU8rU7<2>xU\ 2zV0zX0<5>yi0yk0xn0<2>xt0ww0vw1<8>fxIexKcyL<2>ZyRXyTXyU<16>WyoWypWyq<2>W\ yuVzwWww<8>lOwmKwoGw<3>w0w<9>e0kc0ja0h<2>W0eU0cU0c<118>TQTTQTTRT<3>SSS00\ 0000 } CalculationEffects { ; z->z^4(0+i)*z^2C ; Are the horizontal black lines artifacts of calculation? ; Fractint Version 2003 Patchlevel 1 reset=2003 type=formula formulafile=exprmntl.frm formulaname=Bimandeloid passes=1 center-mag=-1.03683/0.332464/5.806702 params=4/2/0/1/400/3 float=y maxiter=2000 inside=0; colors=@spectrum.map colors=000zzzc00<7>o00p00r00s00u00w00<9>lIBjJCiLD<3>dTI<4>nTApU8rU7<2>xU\ 2zV0zX0<5>yi0yk0xn0<2>xt0ww0vw1<8>fxIexKcyL<2>ZyRXyTXyU<16>WyoWypWyq<2>W\ yuVzwWww<8>lOwmKwoGw<3>w0w<9>e0kc0ja0h<2>W0eU0cU0c<118>TQTTQTTRT<3>SSS00\ 0000 } =================END PARS=============================== =================BEGIN FRM============================== Bimandeloid{ ; vary C over the screen in z->z^A+k*z^B+C ; p1=(A,B)[reals],p2=k[complex],p3=(bailout-4,#critical points) IF(isinit==0) ; image-wide initialization section isinit=1 A = real(p1), B = imag(p1), k = p2 bailout = real(p3) + 4, cps = trunc(imag(p3)) IF(cps<=0) ; give a default value for entry of 0 cps = 1 + ceil(abs(A - B) ) ; works for integers only ENDIF is_agtb = (A > B), diff = abs(A - B), angle = 2 * pi / diff rotfactor = cos(angle) + flip(sin(angle)) IF(is_agtb) ; principal roots of the eqn for cps principal = (-B * K / A) ^ diff ELSE principal = (-A / B / k) ^ diff ENDIF ENDIF C = pixel ; Mandelbrot-like type z = currcp = 0, cpctr = 1 ; first critical point is z = 0 isdiv = isalldiv = 0 ; flags for current cp and all cps divergence : IF(isdiv) ; last critical point diverged cpctr = cpctr + 1 IF(cpctr > cps) ; finished, with all cps diverging isalldiv = 1 ELSEIF(cpctr == 2) ; second cp is the principal value z = currcp = principal, isdiv = 0 ELSE ; rotate the last cp by angle on the complex plane currcp = currcp * rotfactor z = currcp, isdiv = 0 ENDIF ENDIF IF(isalldiv != 1) z = z^A + k*z^B + C ; main iteration isdiv = ( |z| > bailout) ENDIF isalldiv == 0 } ===================END FRM=========================