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psychicmon
Newbie
Joined: 30 Oct 2007
Posts: 37
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 Posted: 01 Dec 2007 12:00:07 pm Post subject: |
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| i see. How do you exactly do those??? I kind of get it, its supposed to be parametric |
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Zaphod Beeblebrox
Member
Joined: 02 Jul 2007
Posts: 119
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| Posted: 01 Dec 2007 02:27:33 pm Post subject: |
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To create a sort of cool fractal do the following:
[font="courier"]seq(2^N,N,1,6->L1
Y1=L1fPart(X/L1
AxesOff
Xmin=0
Xmax=94
Ymin=0
Ymax=62
The idea behind this is the following:
m((a/m)-floor(a/m)) = a mod m.
So to do this on the calculator, you convert it to:
[font="courier"]MfPart(A/M
Which, by the way can be very useful, especially if you don't have omnicalc. Although, If you are dealing with very large numbers, change it to:
[font="courier"]round(MfPart(A/M),0
Because of the way the TI-OS handles numbers.
Last edited by Guest on 01 Dec 2007 02:27:53 pm; edited 1 time in total |
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luby
I want to go back to Philmont!!
Calc Guru
Joined: 23 Apr 2006
Posts: 1477
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| Posted: 05 Dec 2007 08:15:51 pm Post subject: |
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Well, playing with goose's programs I got a few of my favorite:
[attachment=2028:attachment][attachment=2029:attachment][attachment=2030:attachm
ent]
[attachment=2031:attachment][attachment=2032:attachment][attachment=2033:attachm
ent]
[attachment=2034:attachment][attachment=2035:attachment][attachment=2036:attachm
ent]
In order:
.1√(abs(A²-B²
.1√(A²+B²
.2A²/B²
.01(A+B)3
.01(A-B)3
1/(A-B+(A=B
.01(A²/B+B²/A
.001(B3/A²+A3/B²
1/(A+B)+1/(A-B+(A=B |
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Recursive Acronym
Advanced Member
Joined: 11 Dec 2006
Posts: 499
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| Posted: 05 Dec 2007 08:56:24 pm Post subject: |
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Most people have already seen this, but there is a really cool demonstration of the Sierpinski Triangle Fractal in the manuals to the 82 and the 83 family.
Last edited by Guest on 05 Dec 2007 08:57:05 pm; edited 1 time in total |
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Weregoose
Authentic INTJ
Super Elite (Last Title)
Joined: 25 Nov 2004
Posts: 3976
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| Posted: 06 Dec 2007 01:30:50 am Post subject: |
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Here's one variation that you wouldn't find in the manual:
:{0,0:For(X,1,4
:not(augment(Ans
,augment({1},aug
ment(not(Ans),au
gment({1},Ans→S
:End
:ClrDraw
:0→Xmin:47→Xmax
:0→Ymin:31→Ymax
:DelVar ADelVar
BDelVar CDelVar
DDelVar EFor(X,1
,242
:Line(A,B,C,D
:E+60(1-2LS(X→E
:A→C:A+cos(E°→A
:B→D:B+sin(E°→B
:End:ClrList LS
Not long ago, I had stuffed in my signature a little-altered depiction of the logistic map that I had made with my calculator:
Last edited by Guest on 22 Jul 2010 11:21:02 am; edited 1 time in total |
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thornahawk
μολών λαβέ
Active Member
Joined: 27 Mar 2005
Posts: 569
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| Posted: 07 Dec 2007 11:46:15 pm Post subject: |
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Quote: Most people have already seen this, but there is a really cool demonstration of the Sierpinski Triangle Fractal in the manuals to the 82 and the 83 family.
I had, a few Christmases ago, posted a TI-Basic program that generated Michael Barnsley's fractal. It was essentially a modification of the program you speak of. :)
Of course, it should be easy to extend the program to other iterated function systems...
thornahawk |
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Weregoose
Authentic INTJ
Super Elite (Last Title)
Joined: 25 Nov 2004
Posts: 3976
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| Posted: 08 Dec 2007 03:56:54 am Post subject: |
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There you have it—self-similarity.
This is my version; it's too bad it ended up a lot slower:
DelVar ADelVar B0→Xmin:10→Xmax
-3→Ymin:3→Ymax
ClrDraw
Repeat 0
{1,7,7,85}>2abs(2E2rand-{1,9,23,115→A
A-sum(Ans{A,.8A+.26B,1.15A-.28B,.15A-.04B→A
B-sum(LA{.84B,.78B-.23A-1.6,.76B-.26A-.44,.15B+.04A-1.6→B
Pt-On(Ans,A
End
Last edited by Guest on 22 Jul 2010 11:22:28 am; edited 1 time in total |
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thornahawk
μολών λαβέ
Active Member
Joined: 27 Mar 2005
Posts: 569
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| Posted: 09 Dec 2007 09:54:07 am Post subject: |
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The whirl makes for an interesting sight:
Code:
Input "SIDES:",N \\ number of polygon's sides
.1→B \\ angle of displacement of successive polygons
π(1−2/N)→A
sin(A)/(sin(B)+sin(A+B))→C
πseq(2K+1,K,0,N)/N→L1
cos(L1)→L2
sin(L1)→L1
ClrDraw
-1→Ymin:1→Ymax
-1.5→Xmin
1.5→Xmax
ZSquare
For(P,1,36) \\ number of polygons to nest
For(K,1,N)
Line(L1(K),L2(K),L1(K+1),L2(K+1))
End
For(K,1,N+1)
L1(K)→Z
(Zcos(B)−L2(K)sin(B))C→L1(K)
(Zsin(B)+L2(K)cos(B))C→L2(K)
End
End
thornahawk |
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Weregoose
Authentic INTJ
Super Elite (Last Title)
Joined: 25 Nov 2004
Posts: 3976
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| Posted: 29 Jul 2008 02:26:00 am Post subject: |
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I seriously need to get this off my calc:
‾1→Xmin
Ans→Ymin
2→Xmax
1→Ymax
ClrDraw
1→R
For(C,.5,2,[font="times new roman"]∆X
Repeat I=27 or R<0
1→I
R-[font="times new roman"]∆Y→R
C+Ans[font="times new roman"]i
While I[font="verdana"]≠27 and 2>abs(real(Ans
IS>(I,27
Ans²-Ans
End
End
Line(C,R,C,‾R
Line(1-C,R,1-C,‾R
R+3[font="times new roman"]∆Y→R
End
 Took a little over one minute to draw on the TI-84+SE.
Last edited by Guest on 22 Jul 2010 11:24:04 am; edited 1 time in total |
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Weregoose
Authentic INTJ
Super Elite (Last Title)
Joined: 25 Nov 2004
Posts: 3976
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| Posted: 30 Nov 2008 10:06:58 am Post subject: |
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Mira Fractal
Code:
[goose]Disp "","Input Parameters
Prompt A,B
Input "X=?",C
Input "Y=?",D
Input "Zoom:",E
StoreGDB 1
FnOff
ClrDraw
GridOff
AxesOff
PlotsOff
16/E→Ymax
-Ans→Ymin
Ans+2→Xmin
4-Ans→Xmax
ZSquare
Repeat getKey=45
Pt-On(C,D
Pt-On(C,-D
BD+AC+2(1-A)C²/(C²+1→E
AAns-C+2(1-A)Ans²/(Ans²+1→D
E→C
End
StorePic 1
RecallGDB 1
Disp
[/goose]
 A=0.2, B=1, X=12, Y=0, Zoom:1
 A=0.31, B=1, X=12, Y=0, Zoom:0.8
 A=0.4, B=1, X=12, Y=0, Zoom:1.536
 A=0.7, B=0.9998, X=9, Y=0, Zoom:1.75
 A=0.7, B=0.9998, X=12.1, Y=0, Zoom:1.6
 A=0.7, B=0.9998, X=15, Y=0, Zoom:1.5
Best with an emulator.
Last edited by Guest on 22 Jul 2010 11:17:39 am; edited 1 time in total |
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GloryMXE7
Puzzleman 3000
Active Member
Joined: 02 Nov 2008
Posts: 604
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| Posted: 30 Nov 2008 10:21:21 am Post subject: |
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| shouldnt this be in Ti basic forum |
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simplethinker
snjwffl
Active Member
Joined: 25 Jul 2006
Posts: 700
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| Posted: 30 Nov 2008 03:06:24 pm Post subject: |
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GloryMXE7 wrote: shouldnt this be in Ti basic forum
[post="129733"]<{POST_SNAPBACK}>[/post]
It just so happens to be written in BASIC, but it's more about the images/artwork. |
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Galandros
Active Member
Joined: 29 Aug 2008
Posts: 565
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thornahawk
μολών λαβέ
Active Member
Joined: 27 Mar 2005
Posts: 569
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| Posted: 03 Dec 2008 04:29:54 am Post subject: |
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Ah, Mira's "aesthetic chaos"... brings back a lot of memories.
I really must look for my copy of Lauwerier's book; I haven't gotten around to translating most of the BASIC programs to TI-BASIC because of other stuff to do.
In the meantime, someone might like to translate Sprott's BASIC program in this paper on strange attractors. The program would look like Goose's Mira program, only with a different mapping function.
thornahawk |
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Galandros
Active Member
Joined: 29 Aug 2008
Posts: 565
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| Posted: 04 Dec 2008 05:44:56 pm Post subject: |
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Wow I found one chaotic equation that I read some time ago in a math book. I know some things ^^ that would my friends say about this...
thornahawk wrote: In the meantime, someone might like to translate Sprott's BASIC program in this paper on strange attractors. The program would look like Goose's Mira program, only with a different mapping function. [post="129847"]<{POST_SNAPBACK}>[/post]
Maybe I will search wolfram and other sites for some good fun. Also retrieve that math book and code that...
I did not imagined so many good graphics made fast by calculator. The idea I had was that fractals took too long time for calculator from BASIC...
And I have definitely to discover some good fractal or curves as my desktop image. :biggrin: They look so nice...
Last edited by Guest on 04 Dec 2008 05:48:54 pm; edited 1 time in total |
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Open Topic & United-TI Talk => General Open Topic
