FOTD -- May 19, 2016 (Rating A-7,M-8) Fractal visionaries and enthusiasts: Today's image shows a little of what can be done with minibrots of the seventh order when they are calculated in a new way. The formula will reveal the new way, which I discovered several years ago while making up new random formulas, most of which drew beautiful blank screens. When fractals go above the quintic level, they quickly begin to all look the same, and by the time we reach the tenth order, the difference between orders is hard to notice. But look at what lurks in fractals of the seventh order, (and higher orders as well), when we do something new with them. Not only do we have a near perfect minibrot, but there is a very interesting extended pattern surrounding it, partly derived from the parent quadratic Mandelbrot set. This opens an entire new world of fractal exploration, at least for those who seek minibrots. It is also possible to have fractals of fractional orders without those annoying discontinuities, as well as fractals of negative orders. I have just recently begun exploring this stuff, and I'm sure I'll find more new discoveries, not only with today's formula, but with several new formulas I am working on, but have not yet worked the bugs out of. It's such a pleasant day here at FC that I will skip my regular comments about controversial things and enjoy the final rays of sunshine along with FL and the fractal cats. Today turned out quite pleasant here at Fractal Central, with partly cloudy skies, a temperature of 72F 22C, and sunshine that was brilliant between the clouds. The fractal cats took full advantage of the weather by sleeping through the afternoon, while FL puttered in her garden and I searched the internet for things of interest, which there is no shortage of. The next FOTD will be posted in the not too distant future. Until then, take care, and eventually righteousness will prevail, but how will we recognize it when it does? Jim Muth jimmuth@earthlink.net START PARAMETER FILE======================================= WhoSaid_it_wasDull { ; time=0:04:20.78 SF5 at 200MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip passes=1 center-mag=-1.763934523347755/+0.02813687742880176\ /7.566265e+009/1/-27.5000157382336603/1.05747547\ 304718692e-005 params=7/200000000000000.0/0/0 float=y maxiter=3600 inside=0 logmap=99 periodicity=6 colors=000KFhPGlUGoZHscIwgIzcFr`CjX9bU7VZ9SbBPfDNk\ FKoHIsJFwLDkR9_W6Oa3Cf0TjHimYypmprnhsn_uoSvoJxpByp\ BtoBonBjnBemB`lBWlBRkBMk9Id7EZ5AT36N13H87GEAGKEFQH\ FJDDDAB669038UBVNPYHb_BpaPqdbrgorjmlflgckb_iYXhTTg\ OQfJNVaRKsVQmYWh`accfZflUirPlwKnhXkUhhGteMLLLMIKNG\ JODJPBIQ8HR6GS3GS1PTHYTXfTldVkbWj`XiZYhlTNyP1hVJT`\ `DfqFhmGjjHkgKjdNjaPiZSiWViTXhQ_hNahLc`WdTeeLofEyi\ CukBrmAoo8lq7is6fk7dd7bX8`Q8ZXQOcgEjy47sg6pb6nY6lT\ 6mS6mS6mS7af8RtIVuSYva`wkcxufynbwhZvbVtWRsQNqKJpEG\ oKEqPDrVBs_Atd9vj7wo6xt5yBVfSLZgBRw1Jq6LkBNfFP`KRW\ OSVPTUPUUPVTQWSQWSQXRQYQRZQR_PR_OR`OSaNSbMScMScU_`\ `fZhnXouVnoSniQndOmZMmUKmOImJGjIHgHIdGJbFK_ELXDMUC\ NSCORDMRDLRDKRDIQDHQDGQDEQDDPDCPDAPD9PD8yWytYxoZwk\ _vf`ubbuYctUdsPerLgrGhqCip7jo3ko5ll6mj7mh8ne9ocAoa\ BpZCqXDqVTeegVphToiSojQokPolNomMonLooJnpInqGnrFnsD\ ntCntBnsCo_D_RD`ID`AD`FEd } frm:FinDivBrot-2 { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1): z=(b)*(z*z*fn1(z^(a)+b))+c |z| < esc } END PARAMETER FILE=========================================