|
jehovajah
|
 |
« Reply #150 on: March 12, 2010, 08:33:09 AM » |
|
The wizards staff! A julia of arcane power. He who wields it has power to subdue dragons!
|
|
|
|
Logged
|
May a trochoid of 去逸 iteratively entrain your Logos Response transforming into iridescent fractals of orgasmic delight and joy, with kindness, peace and gratitude at all scales within your experience. I beg of you to enrich others as you have been enriched, in vorticose pulsations of extravagance!
|
|
|
|
jehovajah
|
|
« Reply #151 on: March 12, 2010, 10:58:36 AM » |
|
These sculptures arise out of an exploration of the sin and cos functions and the principle range.
|
|
|
|
|
Logged
|
May a trochoid of 去逸 iteratively entrain your Logos Response transforming into iridescent fractals of orgasmic delight and joy, with kindness, peace and gratitude at all scales within your experience. I beg of you to enrich others as you have been enriched, in vorticose pulsations of extravagance!
|
|
|
|
jehovajah
|
|
« Reply #152 on: March 13, 2010, 01:00:21 PM » |
|
The road to the holy grail is long and winding. Why not fly or go by boat?
|
|
|
|
Logged
|
May a trochoid of 去逸 iteratively entrain your Logos Response transforming into iridescent fractals of orgasmic delight and joy, with kindness, peace and gratitude at all scales within your experience. I beg of you to enrich others as you have been enriched, in vorticose pulsations of extravagance!
|
|
|
|
jehovajah
|
|
« Reply #153 on: March 13, 2010, 01:04:42 PM » |
|
Lets stop for breakfast and fry an egg! Wait what appears in the distance......?
|
|
|
|
Logged
|
May a trochoid of 去逸 iteratively entrain your Logos Response transforming into iridescent fractals of orgasmic delight and joy, with kindness, peace and gratitude at all scales within your experience. I beg of you to enrich others as you have been enriched, in vorticose pulsations of extravagance!
|
|
|
|
jehovajah
|
|
« Reply #154 on: March 13, 2010, 01:11:07 PM » |
|
[x=real(z)
y=imag(z)
s=imaj(z)
a=real(c)
b=imag(c)
d=imaj(c)
r2=1*(|c|+d*d)+0*(|z|+s*s)
t0=1*sqrt(|c|)+0*sqrt(|z|)
|z|<10
|c|<10
s2t=sin(2*t0)
c2t=cos(2*t0)
z=1*r2*(s2t*cos(2*b)+s2t*sin(b)*i+c2t*j)+0*r2*(s2t*cos(2*y)+s2t*sin(y)*i+c2t*j)+0*c+0*z
Have fun with the formula. Maybe you might have an interesting adventure on the way to your holy grail! Yom Tov!
|
|
|
|
Logged
|
May a trochoid of 去逸 iteratively entrain your Logos Response transforming into iridescent fractals of orgasmic delight and joy, with kindness, peace and gratitude at all scales within your experience. I beg of you to enrich others as you have been enriched, in vorticose pulsations of extravagance!
|
|
|
|
jehovajah
|
|
« Reply #155 on: March 16, 2010, 08:49:26 AM » |
|
Grail mandy settles down to lay a mandy egg. But she becomes egg bound right at the crucial dropping point! Argh!!!
|
|
|
|
Logged
|
May a trochoid of 去逸 iteratively entrain your Logos Response transforming into iridescent fractals of orgasmic delight and joy, with kindness, peace and gratitude at all scales within your experience. I beg of you to enrich others as you have been enriched, in vorticose pulsations of extravagance!
|
|
|
|
jehovajah
|
|
« Reply #156 on: March 16, 2010, 09:07:46 AM » |
|
First some variations based on the following grailmandy with the approximations to theta and phi incorrectly applied in the tan and cos versions.
y=sin(imag(z))
s=imaj(z)
b=sin(imag(c))
d=imaj(c)
r2=1*(|c|+d*d)+0*(|z|+s*s)
t0=1*sin(sqrt(|c|))+0*sin(sqrt(|z|))
|z|<10
|c|<10
s2t=sin(2*t0)
t2c=cos(2*t0)
z=1*r2*(s2t*cos(2*b)+s2t*sin(2*b)*i+t2c*j)+0*r2*(s2t*cos(2*y)+s2t*sin(2*y)*i+t2c*j)+0*c+0*z
wherey,b,t0 are approximations to theta and phi.
|
|
|
|
Logged
|
May a trochoid of 去逸 iteratively entrain your Logos Response transforming into iridescent fractals of orgasmic delight and joy, with kindness, peace and gratitude at all scales within your experience. I beg of you to enrich others as you have been enriched, in vorticose pulsations of extravagance!
|
|
|
|
jehovajah
|
|
« Reply #157 on: March 16, 2010, 09:24:37 AM » |
|
ctd
|
|
|
|
Logged
|
May a trochoid of 去逸 iteratively entrain your Logos Response transforming into iridescent fractals of orgasmic delight and joy, with kindness, peace and gratitude at all scales within your experience. I beg of you to enrich others as you have been enriched, in vorticose pulsations of extravagance!
|
|
|
|
jehovajah
|
|
« Reply #158 on: March 16, 2010, 10:26:48 AM » |
|
And now the intended versions for cos and tan.
I deliberately altered the colour palette in the last one. Not so boring n'est ce pas?
|
|
|
|
Logged
|
May a trochoid of 去逸 iteratively entrain your Logos Response transforming into iridescent fractals of orgasmic delight and joy, with kindness, peace and gratitude at all scales within your experience. I beg of you to enrich others as you have been enriched, in vorticose pulsations of extravagance!
|
|
|
|
jehovajah
|
|
« Reply #159 on: March 16, 2010, 02:32:24 PM » |
|
y=sin(z)
s=imaj(z)
b=sin(c)
d=imaj(c)
r2=1*(|c|+d*d)+0*(|z|+s*s)
t0=1*sin(sqrt(|c|))+0*sin(sqrt(|z|))
|z|<10
|c|<10
s2t=sin(2*t0)
t2c=cos(2*t0)
z=1*r2*(s2t*cos(2*b)+s2t*sin(2*b)*i+t2c*j)+0*r2*(s2t*cos(2*y)+s2t*sin(2*y)*i+t2c*j)+0*c+0*z
A set based on this variation of grailmandy now follows.
|
|
|
« Last Edit: March 16, 2010, 02:59:42 PM by jehovajah »
|
Logged
|
May a trochoid of 去逸 iteratively entrain your Logos Response transforming into iridescent fractals of orgasmic delight and joy, with kindness, peace and gratitude at all scales within your experience. I beg of you to enrich others as you have been enriched, in vorticose pulsations of extravagance!
|
|
|
|
jehovajah
|
|
« Reply #160 on: March 16, 2010, 03:10:39 PM » |
|
a cos and a closeup of a sinz. Remember these functions are approximating theta and phi, so other functions that have a link to theta and phi may produce interesting results: for example e^iz.
|
|
|
« Last Edit: March 16, 2010, 05:59:41 PM by jehovajah »
|
Logged
|
May a trochoid of 去逸 iteratively entrain your Logos Response transforming into iridescent fractals of orgasmic delight and joy, with kindness, peace and gratitude at all scales within your experience. I beg of you to enrich others as you have been enriched, in vorticose pulsations of extravagance!
|
|
|
|
|
|
jehovajah
|
|
« Reply #162 on: March 23, 2010, 06:26:06 AM » |
|
Just to finish this part of the exploration, using cosz as an approximation to theta and arranging the formula for a traditional mandy thusly:
y=cos(z)
s=imaj(z)
b=cos(c)
d=imaj(c)
r2=0*(|c|+d*d)+1*(|z|+s*s)
t0=0*cos(sqrt(|c|))+1*cos(sqrt(|z|))
|z|<10
|c|<10
s2t=sin(2*t0)
t2c=cos(2*t0)
z=0*r2*(s2t*cos(2*b)+s2t*sin(2*b)*i+t2c*j)+1*r2*(s2t*cos(2*y)+s2t*sin(2*y)*i+t2c*j)+1*c+0*z
|
|
|
|
Logged
|
May a trochoid of 去逸 iteratively entrain your Logos Response transforming into iridescent fractals of orgasmic delight and joy, with kindness, peace and gratitude at all scales within your experience. I beg of you to enrich others as you have been enriched, in vorticose pulsations of extravagance!
|
|
|
|
jehovajah
|
|
« Reply #163 on: March 28, 2010, 04:46:07 PM » |
|
to finish with grailmandy i have set the formula to reflect mandlebulb formulae, and used sin and tan as approximations for theta, phi.
|
|
|
|
Logged
|
May a trochoid of 去逸 iteratively entrain your Logos Response transforming into iridescent fractals of orgasmic delight and joy, with kindness, peace and gratitude at all scales within your experience. I beg of you to enrich others as you have been enriched, in vorticose pulsations of extravagance!
|
|
|
|
David Makin
|
|
« Reply #164 on: April 03, 2010, 10:13:57 PM » |
|
Just had a really crazy idea and tried it, I didn't expect it would actually "work" and it didn't - you just get a sort of slightly plumped out 2D Mandelbrot, but I like the Julias:
UF code:
magn = sqrt((m=|zri|)+(s=sqr(zj)))
if magn>0.0
zri = sqr(zri)
magn = sqr(magn)/sqrt(sqr(m)+s)
zri = magn*zri + cri
zj = magn*zj + cj
else
zri = cri
zj = cj
endif
zri/cri are complex, magn/zj/m/s are real and in UF |zri| means the magnitude of zri squared.
|
|
|
|
|
Logged
|
|
|
|
|
January 09, 2012, 07:29:16 PM
Dilber MC Theme by HarzeM