At 11:49 AM on 11/29/04 I wrote:

...

(The hypercomplex Mandelbrot formula has the same parameter limitation, though in that case I have written my own formula that includes some of the missing parameters and draws some very curious and interesting images.)

Hiram Berry replied:

By all means please post it!

Here is my reworking of the Hypercomplex Mandelbrot formula. When (p1) and (p2) are kept at 0,0 the third parameter draws the same hypercomplex images as the hard-coded formula when the function is set to 'sqr'. The included parameter file gives an example of some of the unexpected things the formula does. I have barely tapped the potential of this formula. Jim M. START PARAMETER FILE======================================= Hyper-Mandelbrot { ; time=0:00:31.59--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=HyperMandelbrot passes=1 center-mag=-0.56964/0/0.8503401 params=0/0/3/0/\ 1e-010/0 float=y maxiter=1000 bailout=9 inside=0 logmap=yes symmetry=none periodicity=none colors=000dIPbGT`EWdDcgCjkBln2mp8nqDnsJitOeuU`wZWx\ dRyiNweHudCsc6qb1oaZm`nk`ii`dg``e`WcbRabN__MYWMWRL\ UMLSHLQDKO9KM5KKAOKERQIUWMXaR`gVcmZfrbinWmjQqfJubD\ x`Gv_JuZLsYOrWRpVToUWnTZlR`kQciPfhOhgQgdSfaUfZWeWY\ dT_dQacNbcLeXFcYGaYH`ZHZZIX_JW_JU_KS`LR`LPaML`QNaN\ MbNKbOkcEhbFfbGdbHbbI_bIYbJWbKUbLRbLPbMNbNLbOCtKEq\ LFnMGkMHhNIeOAxjCtfDpbFmZGiVIeRJcAJbEJbHJbLjOUfQTc\ SS`TSYVRVXQSYQP_PMaOX6uUCoSHiQNdNSZLYTHZvI`sIbpIdm\ IfjIhgIjdJiaJhZJfWJeTJcQqF`mIZjKYfNXcPV_RUXUTTWRQZ\ QM`PvewrdsndojdlfchbceZcaVbYRbVNbRJF7JRGkKOiMOgNOe\ OOcQOaRO_SOYTOWVOUWOSXOQYOO_OM`OKaOPpTOoSOnSNmSNlU\ NkXMj_MibLheLghLfkKenKdqJctJbwF9zGEzHIzHMzIRzIVzJZ\ zt9zpCzmEzjHzgJzdMzaOzYRzVTzSWzPYzM`zCpzDnzElzFkzG\ izGhzHfzIezJczchz`hzZhzXhzUhzShzQhzNhzLhzVhzQhzPhz\ OhzOhzNhzNhzMhzLhzLhzKhzKhzJhzFhzGhzGhzGhzHhzHhzHh\ zIhzIhzIhzJhzJhzkhzihzghz } frm:HyperMandelbrot {; periodicity must be turned off a=(p1),b=(0,0): q=sqr(a)-sqr(b)+pixel, b=(p2+2)*a*b+p3, a=q, |a|+|b| <= 100 } END PARAMETER FILE=========================================