Dr. J, got too much sun over the weekend. Now it is effecting his behavior. The latest is, well, he is really mad at me for not helping him with a math problem. Believe me, I tried, but email being slow and even though my friends are helpful... Anyway, he got into a quarrel with a FractoBall official about a call in the last FractoBowl game.
Oh, his sun burn? Have you ever met someone who no matter how much sun burn they look like they have, they don't peel. They just suddenly have a nice tan. Well, that is Dr. J., Figure 1. He has forgotten about the Sunday's sunburn, and it is only Tuesday!
Oh yes, where was I...
Oh yes, the FractoBall feud. It seem there was a bad call, er... a questionable call. You see, if a player touches out of bounds he is out of the play. And since the FractoBall field is not a rectangle, and refereeing can be problematic. There seems to always be a discussion (they call it an iteration) about these plays. On some of these border line plays, discussions can carry on into billions of iterations.
Now these iterations take on a routine flavor after a while. And if they settle to a single result, then the player is considered 'in'. But if it settles into a repeating cycle of two or more values, the discussion is considered unfocused (well, that is what they call it) and the player is 'out' of bounds. The formula for the iterations used in the games is
1) z= z3 + c
|
Figure 1. Dr. J has a nice tan after all.
 |
Figure 2. An idealized FractoBall field.
The FractoBall field has a fat figure 8 shape. Fans collect in the heart shaped cells around the field. The boundary of the actual playing field is, in complex arithmetic given by this formula, describing a cycloid.
Let
2) z = exp(i*pi*theta)/sqrt(3);
Then
3) c = z(1-z2).
Theta (the Greek letter) is an angle which allows us to trace out the boundary. This equation is used to make the original field markings. But then as the game proceeds, the marks get messed up. The players kick up a lot of Fatou dust. When a doubtful play occurs, a flag thrown down by an official marks the questionable spot. After using an equivalent of GPS (Global Positioning System) the officials obtain the complex coordinate value for the mark. Application of Eqn 1, iterated until a result can be reached, decides all.
In the last game, a very long almost non-terminating iteration occurred with tempers flaring as the minutes passed. Dr. J had become very irate about this. He was in fact scolded by an official for shouting and jeering. But he tells me it is unfair. (no duh, right). The cameras actually recorded that spat on the sidelines, there not being much else to cover.
Anyway, Dr. J claimed "I can make these questionable play calls in one iteration!"
They said "Prove it! or sit down!!"
Dr. J has been fuming ever since. "What do they know", he sputters. I have asked by email if he actually has a better way to make the call. He just sputtered, of course. Sputtered? you ask? on email? Well here is a sample of his email:
Of cORse i Can HOw daRE you QUestIOn Dr J! MaYBe ILL teLL you, MaYBe I woNT.
I'm sure I can sort this out for us in the real world tomorrow. Until
then...
Stay healthy,
Jay
FGZ-Mand { ; (c) Jay Hill, 1998
IF( |p3| == 0)
p3 = 16
ENDIF
c=pixel, z=sqrt(-c), bailout = real(p3):
z1=z*z + c;
z = p1*z1*z1/(z1 + p2) + c;
|z| <= bailout
}
FGZ-M-DrJ-Sun-Burn { ; (c) Jay Hill, 1998
reset=1960 type=formula formulafile=fgz.frm formulaname=fgz-mand
center-mag=-0.02796925726298376/-0.00024404017074993/177.1369/1/-90
params=16/0/0.1/0/0/0 float=y maxiter=2560 inside=bof61 outside=128
decomp=256
colors=mU0kT1UA3cK3XA6bN6AAAcL5RA4cK\
4A43SG3K62OE2UD1KB0UB0cA0UA0F90U80D7\
0K70B60<4>520320210000000<4>321K2143\
1<87>mcKcmKmcK<125>000
}
frm:Colorit-3 { ; (c) Jay Hill, 1998
b=p1 ; p1=cos(a)+i*sin(a), a=light angle
if(p1==0)
p1=1
endif
a=pi*p1/180, b=cos(a)+i*sin(a) ; p1= light angle (deg)
done = 1, iter=0, z = 0, zc = 0, c = pixel, dz=1
: ; initialization.
iter = iter+1 ; gotta count em
dz=3*sqr(zc)*dz+1 ; derivative, dz/dc
zc=zc*sqr(zc) + c ; standard MSet iteration
if(|zc| >= 1024) ; Bailout
z = z -8 + ((sin(2*pi*iter/256)*Real(b*dz/zc))>0) + iter
done=-1 ; Set flag to force an exit.
endif
done >= 0 ; Continue if the flag >=0.
}
FractoBall-field { ; (c) Jay Hill, 1998 FractoBall field
reset=1960 type=formula formulaname=colorit-3
center-mag=-8.88178e-016/-6.66134e-016/0.9861933/1/-90 params=120/0
float=y maxiter=2560 inside=0 outside=real periodicity=0
colors=UcAVTTcccVTTcccVTTcccVTTcccVTTcccVTTcccVTTcccVTTcccVTTcccVTTcccUU\
UcccUUUccc0mK0U02mJ1U05nI3U07nH5V0AoG6V0CoF8W0FpDAW0IqCCX0KqBDX0NrAFX0Pr\
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}
