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 Post subject: Julia set.
PostPosted: Sat Sep 01, 2018 5:14 pm 
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Joined: Mon May 25, 2015 1:12 pm
Posts: 92
I keep on seeing people running Mandlebrot sets on their homebrew computers, but I don't see many other fractals being run so... Here's my Julia set. I'm sure the brains trust could geatly improve it.

Anyway, here's the (Not very clever) code to generate it, including a little boilerplate for my machine to not mess up the terminal window with.

Code:
1 zoom = 35
5 BITCLR $5E0,0: PRINT CHR$(12); : REM Serial out off, and clear screen.
10 creal=-0.8
20 cimag=0.156
30 FOR v=-48 TO 48
40 FOR h=-78 TO 78
50 x=h/(zoom*2)
60 y=v/zoom
70 FOR i=1 TO 50
80 zreal=x*x-y*y+creal
90 zimag=x*y*2+cimag
100 IF zreal*zreal>1000 THEN GOTO 150
110 x=zreal
120 y=zimag
130 NEXT i
140 px=h+79: py=v+49: GOSUB 4000
150 NEXT h
160 NEXT v
165 BITSET $5E0,0 : REM Serial out on again.
170 END
3997 :
3998 REM Plot
3999 :
4000 PRINT CHR$(5);CHR$(px);CHR$(py);
4010 RETURN


I wonder what else is out there, maybe a strange attractor?


Attachments:
ToE-Julia.jpg
ToE-Julia.jpg [ 229.7 KiB | Viewed 11656 times ]
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 Post subject: Re: Julia set.
PostPosted: Sat Sep 01, 2018 5:38 pm 
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Joined: Thu Dec 11, 2008 1:28 pm
Posts: 10793
Location: England
Looks nice!

Is that CHR$(5) plot routine something you've added to EhBasic? Or is there perhaps a VDU driver component to your system? Does it have more capabilities?
(I had a quick look in your Tower of Eight repo but didn't find an answer.)


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 Post subject: Re: Julia set.
PostPosted: Sat Sep 01, 2018 5:47 pm 
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Since the video-card my ToE is running at the moment is based on Grant Searles code, which is itself a derivative, it comes from there. Basically, I've got a set of bits that determine where output gets forwarded to. I plan to add some extra software to draw lines and circles to the OS too. I didn't put Grant's code in my repo because he's not replied to my request to do so. There are other graphics cards I could be using but one doesn't work yet (struggling with timing issues and tooling issues on FPGA) and the other one doesn't have Tower OS support yet.

Whilst I don't think Grant would mind, he does explicitly forbid publishing it without his permission.


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 Post subject: Re: Julia set.
PostPosted: Sat Sep 01, 2018 6:16 pm 
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Ah, thanks. I'm sure Grant wouldn't mind a link though.


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 Post subject: Re: Julia set.
PostPosted: Sat Sep 01, 2018 6:18 pm 
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So... how long does it take to plot the 15000 or so pixels?


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 Post subject: Re: Julia set.
PostPosted: Sat Sep 01, 2018 6:21 pm 
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Depends at which clock rate I've chosen at the tine. I guess (and I've not timed it yet) probsbly around 20 minutes. Nothing like that incredible one foe the BBC.


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 Post subject: Re: Julia set.
PostPosted: Sat Sep 01, 2018 6:35 pm 
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A strange attractor is a good idea: something where most of calculations result in plotting a point, rather than something where each point needs heaps of calculations.


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 Post subject: Re: Julia set.
PostPosted: Sat Sep 01, 2018 6:40 pm 
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I wrote a strange attractor based on some psuedocode I found in a book some time ago. Mind you, that was in FORTH on a Speccy. It'd probably only take an afternoon to get going.

There's also things like the Sierpinski Triangle that wouldn't look too bad on said low res screen.


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 Post subject: Re: Julia set.
PostPosted: Sat Sep 01, 2018 7:36 pm 
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@BigEd, I just added said link to the ToE wiki.


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 Post subject: Re: Julia set.
PostPosted: Sat Sep 01, 2018 9:52 pm 
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There's also the "chaotic bifurcation" formula. There's an interesting discussion of this (in a Python context) here: https://ipython-books.github.io/121-plotting-the-bifurcation-diagram-of-a-chaotic-dynamical-system/


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 Post subject: Re: Julia set.
PostPosted: Sat Sep 01, 2018 9:54 pm 
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We had one of those in BBC Basic over on stardot:
https://stardot.org.uk/forums/viewtopic ... 00#p200300


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