|
Fractal of the Day
by Jim Muth
|
|
Fractal visionaries and enthusiasts: On a recent visit with fractal lady to one of the nearby antique emporiums, I came upon an old book printed in 1856 and titled "Wells's Familiar Science". Being in a state of moderate boredom, I opened it and found it to be a book of popularized science as science was understood in the middle of the 19th Century, with the text presented in a question-and-answer format. Since the price was quite reasonable, I purchased the book, which now lies on the desk beside me. I have yet to read it thoroughly, but the small part I have browsed through is quite interesting. It is surprising how much our scientific understanding of some phenomena have changed in the past 152 years, and how little our understanding of other phenomena have changed. The velocity of light is given as around 190,000 miles per second, a bit too fast. And there is a section explaining the constitution of the so-called luminiferous ether. One of the greatest questions about light at the time was what happens to it when it is absorbed by a dark body. The source of the sun's energy was a complete mystery, though it was speculated that the sun emits heat and light as a bell emits sound when it is struck, without exhausting its reservoir of sound. I'll relate further interesting tidbits from the book as I come upon them, but now we have a fractal to investigate. The fractal was generated by calculating the formula Z^(1.375)+C at a level 1.375 units down the logarithmic ladder, while applying no function. I'll not describe the parent fractal in much detail. It is basically a distorted Mandeloid standing on its head. Today's unusually gaudy scene is located in a small valley near the parent fractal's 'nose'. I gave the image the rather poetic name, "Under the Equinox", though I have since forgotten what moved me to give it this name. The rating of an 8 might be a bit optimistic, especially for an image with no true minibrot at its center. The central blue triangle is no real substitute. To add some extra zip, the image was rendered with the outside set to 'tdis'. The calculation time of 16-1/3 minutes is admittedly slow, but instant gratification is available on the FOTD web site at: Steady rain all day and a very un-springlike temperature of 52F 11C made Friday a day to be forgotten here at Fractal Central. The duo of fractal cats watched the dripping water for a few minutes, then viciously attacked their catnip rats and mice. My day was close to normal. The next semi-glorious FOTD will appear in 24 hours or so. Until then, take care, and don't be too sure of things you're not sure of. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Under_the_Equinox { ; time=0:16:21.46-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
formulaname=MandelbrotBC3 function=ident inside=255
center-mag=+0.05758293098342480/-0.989073028706620\
60/2.569865e+007/1/152.5/0 params=1.375/0/-1.375/0
maxiter=2200 outside=tdis logmap=1175 periodicity=10
float=y passes=1
colors=000HJ4HN4HY4Hf4Nm2Ym2fn1qn1zq0zq0zs0zs0zu0z\
y0zw0qu0fs0Yq0Nn0Jn0Lm0Lk0Li0Nf0Nf0Ne0Pc0Pa0PZ0SZ0\
SY0SW0UU0US0US0UP0WN0WL0WJ0YJ0YH0YG0ZE0ZC0ZC0aA0a8\
0a60m40w40z20zU0zZ0zZ0y00k10Z20Y40W60U80SA0PC0NE0L\
G0JH0HJ0GL0EN06W0CP0HL0LH0SE0YA0a62f26k0Cq0Gw0Jz0P\
z0Uz0Yz0Uz0Sy0Pw0Ns0Ln0Jk0Hi0Ee0Ca0AY08W06S04N02L0\
1H00E10A108204201400600600800800A00C00C00E00E00C00\
C00C00C00C00C00C00C00C00C00A00A20A40A80AA0AC0AG0AH\
0AL0AN08S08U08W08Z08a08e08f08k08m08n0Am0Am0Am0Ak0A\
k0Ak0Ai0Ai0Ai0Ai0Af0Af0Af0Ae0Ae0Ae0Ae0Ac0Ac0Ac0Aa0\
Aa0Aa0Aa0AZ0AZ0AZ0AY0AY0AY0AY0AW0AW0AW0AU0AU0AU0AU\
0AS0AS0AS0AP0AP0AP0AP0CN0CL0EJ0EJ0GH0GG0HG0HE0JC0J\
A0LA1L84N66N68P4AP2ES1GS1HU0LU0NW0PW0UY0WY0YZ0aZ0c\
a0ea0fc0kc0me0ne0sf0uf0wi0zi0zk0zk0zm0zm0zn0zn0zm0\
zm0zk0zk0zi0zi0zf0wf0qf0me0ke0fc0ec0ca0Za0YZ0WZ0SZ\
0PY0NY0JW0HW0GU0CU0AU08zz }
frm:MandelbrotBC3 { ; by several Fractint users
e=p1, a=imag(p2)+100
p=real(p2)+PI
q=2*PI*fn1(p/(2*PI))
r=real(p2)+PI-q
Z=C=Pixel:
Z=log(Z)
IF(imag(Z) > r)
Z=Z+flip(2*PI)
ENDIF
Z=exp(e*(Z+flip(q)))+C
|Z| < a }
END PARAMETER FILE=========================================
|
times.
