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Author Topic: Original IFS Fractals  (Read 5179 times)

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Offline AndyA

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Original IFS Fractals
« on: December 09, 2019, 12:32:08 am »
These are fractals that I've designed, so you  haven't seen them before, although some may look like others on the net.
All of them were designed in Apophysis https://sourceforge.net/projects/apophysis/files/latest/download
except for the 'QB64' IFS fractal.

'QB64' was designed using IFS Lab  https://www.nzeldes.com/Fractals/Fractals_core.htm
Both of the software packages are free downloads.

@Johnno56 and Bplus,
I hope these render better than the ones in SDL Basic, they're super fast on QB64!

On my machine all fractals except QB64 render in a millisecond or less!



QB64   (needs a steady hand so it doesn't look like a child drew it. Oh well...)
Code: QB64: [Select]
  1. 'Original IFS fractal by Andy Amaya
  2. 'Designed in 'IFS Lab' by Nathan Zeldes     https://www.nzeldes.com/Fractals/Fractals_core.htm
  3. _TITLE "IFS QB64"
  4.  
  5. scaleX! = 850.0
  6. scaleY! = 1200.0
  7. offsetX% = -25
  8. offsetY% = -20
  9. SCREEN _NEWIMAGE(800, 600, 32)
  10. CLS , _RGB32(0, 0, 96)
  11. COLOR _RGB32(255, 255, 255)
  12.  
  13. FOR iter& = 0 TO 80000
  15.         CASE 0 TO .1106
  16.             nx! = 0.240 * lastX! + 0.005 * lastY! + 0.057
  17.             ny! = 0.002 * lastX! + 0.170 * lastY! + 0.087
  18.         CASE .1107 TO .1982
  19.             nx! = -0.002 * lastX! + 0.139 * lastY! + 0.066
  20.             ny! = -0.231 * lastX! + -0.008 * lastY! + 0.384
  21.         CASE .1983 TO .3092
  22.             nx! = 0.242 * lastX! + 0.005 * lastY! + 0.056
  23.             ny! = -.009 * lastX! + 0.168 * lastY! + 0.363
  24.         CASE .3093 TO .3238
  25.             nx! = 0.055 * lastX! + -0.047 * lastY! + 0.302
  26.             ny! = 0.052 * lastX! + 0.053 * lastY! + 0.384
  27.         CASE .3239 TO .41491
  28.             nx! = 0.003 * lastX! + 0.142 * lastY! + 0.343
  29.             ny! = -0.235 * lastX! + -0.005 * lastY! + 0.374
  30.         CASE .4150 TO .4377
  31.             nx! = 0.063 * lastX! + -.068 * lastY! + 0.445
  32.             ny! = 0.064 * lastX! + 0.065 * lastY! + 0.106
  33.         CASE .4378 TO .4640
  34.             nx! = 0.071 * lastX! + -.068 * lastY! + 0.438
  35.             ny! = 0.074 * lastX! + 0.065 * lastY! + 0.251
  36.         CASE .4641 TO .4842
  37.             nx! = 0.074 * lastX! + 0.003 * lastY! + 0.349
  38.             ny! = 0.000 * lastX! + 0.100 * lastY! + 0.096
  39.         CASE .4843 TO .5033
  40.             nx! = 0.075 * lastX! + -0.005 * lastY! + 0.351
  41.             ny! = 0.000 * lastX! + 0.094 * lastY! + 0.358
  42.         CASE .5034 TO .5837
  43.             nx! = 0.001 * lastX! + 0.131 * lastY! + 0.221
  44.             ny! = -0.226 * lastX! + -0.010 * lastY! + 0.374
  45.         CASE .5838 TO .6073
  46.             nx! = 0.071 * lastX! + 0.058 * lastY! + 0.394
  47.             ny! = -0.048 * lastX! + 0.083 * lastY! + 0.227
  48.         CASE .6074 TO .6280
  49.             nx! = 0.058 * lastX! + 0.066 * lastY! + 0.405
  50.             ny! = -0.033 * lastX! + 0.094 * lastY! + 0.355
  51.         CASE .6281 TO .7096
  52.             nx! = 0.058 * lastX! + 0.191 * lastY! + 0.540
  53.             ny! = -0.152 * lastX! + 0.018 * lastY! + 0.229
  54.         CASE .7097 TO .7481
  55.             nx! = 0.015 * lastX! + 0.099 * lastY! + 0.538
  56.             ny! = -0.140 * lastX! + 0.021 * lastY! + 0.353
  57.         CASE .7482 TO .7783
  58.             nx! = 0.119 * lastX! + 0.003 * lastY! + 0.575
  59.             ny! = 0.003 * lastX! + 0.094 * lastY! + 0.344
  60.         CASE .7784 TO .8416
  61.             nx! = 0.197 * lastX! + -0.034 * lastY! + 0.751
  62.             ny! = 0.000 * lastX! + 0.118 * lastY! + 0.199
  63.         CASE .8417 TO .8706
  64.             nx! = 0.117 * lastX! + -0.036 * lastY! + 0.607
  65.             ny! = 0.061 * lastX! + 0.073 * lastY! + 0.214
  66.         CASE .8707 TO .8819
  67.             nx! = 0.016 * lastX! + 0.071 * lastY! + 0.661
  68.             ny! = -0.051 * lastX! + 0.031 * lastY! + 0.343
  69.         CASE .8820 TO .9174
  70.             nx! = 0.043 * lastX! + 0.09 * lastY! + 0.759
  71.             ny! = -0.128 * lastX! + 0.034 * lastY! + 0.198
  72.         CASE .9175 TO .9499
  73.             nx! = 0.003 * lastX! + 0.095 * lastY! + 0.853
  74.             ny! = -0.125 * lastX! + 0.008 * lastY! + 0.206
  75.         CASE ELSE
  76.             nx! = 0.006 * lastX! + 0.123 * lastY! + 0.846
  77.             ny! = -0.149 * lastX! + 0.008 * lastY! + 0.387
  78.     END SELECT
  79.     IF iter& > 20& THEN PSET (nx! * scaleX! + offsetX%, ny! * scaleY! + offsetY%)
  80.     lastX! = nx!
  81.     lastY! = ny!
  85.  

Moon Jelly
Code: QB64: [Select]
  1. 'Original IFS fractal by Andy Amaya
  2. 'ap4-180109-001a
  3. _TITLE "IFS Moon Jelly"
  4.  
  5. scaleX! = 85.916
  6. scaleY! = 109.973
  7. offsetX% = 564
  8. offsetY% = 61
  9. SCREEN _NEWIMAGE(800, 600, 32)
  10. CLS , _RGB32(0, 0, 170)
  11. COLOR _RGB32(128, 240, 255, 64)
  12.  
  13. FOR iter& = 0 TO 1000000
  15.         CASE 0 TO .24
  16.             nx! = -.486478 * lastX! + -.886276 * lastY! + -2.09443
  17.             ny! = -.543314 * lastX! + .977109 * lastY! + -.609152
  18.         CASE .25 TO .49
  19.             nx! = .299017 * lastX! + .018083 * lastY! + -.881445
  20.             ny! = .079087 * lastX! + .396048 * lastY! + .208439
  21.         CASE .50 TO .74
  22.             nx! = .582294 * lastX! + -.618687 * lastY! + .854146
  23.             ny! = .32754 * lastX! + .315409 * lastY! + .8567
  24.         CASE ELSE
  25.             nx! = .585919 * lastX! + .019146 * lastY! + -1.30101
  26.             ny! = -.351028 * lastX! + .260532 * lastY! + .211793
  27.     END SELECT
  28.     IF iter& > 20& THEN PSET (nx! * scaleX! + offsetX%, ny! * scaleY! + offsetY%)
  29.     lastX! = nx!
  30.     lastY! = ny!


Foot Print (closest description I could think of)
Code: QB64: [Select]
  1. 'Original IFS fractal by Andy Amaya
  2. 'ap3-180106-221
  3. _TITLE "IFS Foot Print"
  4.  
  5. scale! = 545.6813
  6. offsetX% = 144
  7. offsetY% = 355
  8. SCREEN _NEWIMAGE(800, 600, 32)
  9. CLS , _RGB32(224, 192, 120)
  10. COLOR _RGB32(160, 118, 96, 50)
  11.  
  12. FOR iter& = 0 TO 1000000
  14.         CASE 0 TO .177
  15.             nx! = -.256576 * lastX! + -.270262 * lastY! + .566841
  16.             ny! = -.211468 * lastX! + .270545 * lastY! + -.332541
  17.         CASE .178 TO .307
  18.             nx! = .19207 * lastX! + -.402232 * lastY! + .344923
  19.             ny! = -.256814 * lastX! + -.39666 * lastY! + .266384
  20.         CASE ELSE
  21.             nx! = .623372 * lastX! + .245593 * lastY! + .158646
  22.             ny! = -.188462 * lastX! + .908327 * lastY! + .075229
  23.     END SELECT
  24.     IF iter& > 20& THEN PSET (nx! * scale! + offsetX%, ny! * scale! + offsetY%)
  25.     lastX! = nx!
  26.     lastY! = ny!

Fossil Leaf  (maybe like drawings from ancient Greece)
Code: QB64: [Select]
  1. 'Original IFS fractal by Andy Amaya
  2. 'ap3-180111-067
  3. _TITLE "IFS Fossil Leaf"
  4.  
  5. scale! = 171.035
  6. offsetX% = 357
  7. offsetY% = 343
  8. SCREEN _NEWIMAGE(800, 600, 32)
  9. CLS , _RGB32(160, 160, 144)
  10. COLOR _RGB32(80, 64, 64, 50)
  11.  
  12. FOR iter& = 0 TO 1000000
  14.         CASE 0 TO .352
  15.             nx! = .202353 * lastX! + -.639381 * lastY! + .268058
  16.             ny! = .177023 * lastX! + .271414 * lastY! + .786708
  17.         CASE .353 TO .387
  18.             nx! = -.635039 * lastX! + .15876 * lastY! + -.049461
  19.             ny! = .575503 * lastX! + -.178604 * lastY! + .042522
  20.         CASE ELSE
  21.             nx! = .115852 * lastX! + -.739359 * lastY! + .379494
  22.             ny! = -.891958 * lastX! + -.126396 * lastY! + -.300873
  23.     END SELECT
  24.     IF iter& > 20& THEN PSET (nx! * scale! + offsetX%, ny! * scale! + offsetY%)
  25.     lastX! = nx!
  26.     lastY! = ny!

Recursive Tree
Code: QB64: [Select]
  1. 'Original IFS fractal by Andy Amaya
  2. 'ap3-180114-200
  3. _TITLE "IFS Recursive Tree"
  4.  
  5. scale! = 219.7
  6. offsetX% = 335
  7. offsetY% = -9
  8. SCREEN _NEWIMAGE(800, 600, 32)
  9. CLS , _RGB32(8, 8, 80)
  10. COLOR _RGB32(16, 224, 16, 32)
  11.  
  12. FOR iter& = 0 TO 1000000
  14.         CASE 0 TO .49
  15.             nx! = .705963 * lastX! + .358987 * lastY! + -.842529
  16.             ny! = -.358987 * lastX! + .705963 * lastY! + .287289
  17.         CASE .50 TO .98
  18.             nx! = .742239 * lastX! + -.300776 * lastY! + .905319
  19.             ny! = .300776 * lastX! + .742239 * lastY! + .118988
  20.         CASE ELSE
  21.             nx! = -.004846 * lastX! + -.006989 * lastY! + .388043
  22.             ny! = .510377 * lastX! + .510208 * lastY! + .73348
  23.     END SELECT
  24.     IF iter& > 20& THEN PSET (nx! * scale! + offsetX%, ny! * scale! + offsetY%)
  25.     lastX! = nx!
  26.     lastY! = ny!

Gnarled Tree
Code: QB64: [Select]
  1. 'Original IFS fractal by Andy Amaya
  2. 'ap6-171203-84f
  3. _TITLE "IFS Gnarled Tree"
  4.  
  5. scaleX! = 194.287
  6. scaleY! = 149.698
  7. offsetX% = 352
  8. offsetY% = 291
  9. SCREEN _NEWIMAGE(800, 600, 32)
  10. CLS , _RGB32(0, 0, 0)
  11. COLOR _RGB32(96, 32, 16, 64)
  12.  
  13. FOR iter& = 0 TO 1000000
  15.         CASE 0 TO .159
  16.             nx! = .598158 * lastX! + -.356052 * lastY! + .67161
  17.             ny! = .356052 * lastX! + .598158 * lastY! + -.648611
  18.         CASE .16 TO .319
  19.             nx! = -.448094 * lastX! + .308849 * lastY! + -.502771
  20.             ny! = .365187 * lastX! + .577554 * lastY! + -.608248
  21.         CASE .32 TO .479
  22.             nx! = .006326 * lastX! + -.143369 * lastY! + -.064071
  23.             ny! = -.60489 * lastX! + .328351 * lastY! + .96276
  24.         CASE .48 TO .639
  25.             nx! = .299832 * lastX! + -.365076 * lastY! + .831409
  26.             ny! = .365076 * lastX! + .299832 * lastY! + .150385
  27.         CASE .64 TO .799
  28.             nx! = -.323505 * lastX! + .327934 * lastY! + -.647351
  29.             ny! = .358033 * lastX! + .437453 * lastY! + .205967
  30.         CASE ELSE
  31.             nx! = .066005 * lastX! + .050959 * lastY! + -.10212
  32.             ny! = .121996 * lastX! + -.32715 * lastY! + .704038
  33.     END SELECT
  34.     IF iter& > 20& THEN PSET (nx! * scaleX! + offsetX%, ny! * scaleY! + offsetY%)
  35.     lastX! = nx!
  36.     lastY! = ny!
  40.  


Another tree without leaves
Code: QB64: [Select]
  1. 'Original IFS fractal by Andy Amaya
  2. 'ap6-171203-84h
  3. _TITLE "IFS Fall Tree"
  4.  
  5. scaleX! = 131.734
  6. scaleY! = 88.0348
  7. offsetX% = 344
  8. offsetY% = 337
  9. SCREEN _NEWIMAGE(800, 600, 32)
  10. CLS , _RGB32(0, 0, 0)
  11. COLOR _RGB32(96, 32, 16, 64)
  12.  
  13. '[Parms]  6,  168.6201,  112.6828,  440,  431
  14. ' .620647,-.31522, .31522, .620647, .891658,-.742917, .16
  15. '-.554868, .059819, .162085, .652211,-.005441,-1.35337, .16
  16. '-.017134,-.064781,-.590634, .429267, .103238, 1.25386, .16
  17. ' .299832,-.365076, .365076, .299832, .950864, .024643, .16
  18. '-.334892, .313644, .347405, .44781,-.632132, .023339, .16
  19. '-.070131, .022771, .301621,-.427331, .085163, 1.02988, .16
  20.  
  21.  
  22. FOR iter& = 0 TO 1000000
  24.         CASE 0 TO .159
  25.             nx! = .620647 * lastX! + -.31522 * lastY! + .891658
  26.             ny! = .31522 * lastX! + .620647 * lastY! + -.742917
  27.         CASE .16 TO .319
  28.             nx! = -.554868 * lastX! + .059819 * lastY! + -.005441
  29.             ny! = .162085 * lastX! + .652211 * lastY! + -1.35337
  30.         CASE .32 TO .479
  31.             nx! = -.017134 * lastX! + -.064781 * lastY! + .103238
  32.             ny! = -.590634 * lastX! + .429267 * lastY! + 1.25386
  33.         CASE .48 TO .639
  34.             nx! = .29983 * lastX! + -.365076 * lastY! + .950864
  35.             ny! = .365076 * lastX! + .299832 * lastY! + .024643
  36.         CASE .64 TO .799
  37.             nx! = -.334892 * lastX! + .313644 * lastY! + -.632132
  38.             ny! = .347405 * lastX! + .44781 * lastY! + .023339
  39.         CASE ELSE
  40.             nx! = -.070131 * lastX! + .022771 * lastY! + .085163
  41.             ny! = .301621 * lastX! + -.427331 * lastY! + 1.02988
  42.     END SELECT
  43.     IF iter& > 20& THEN PSET (nx! * scaleX! + offsetX%, ny! * scaleY! + offsetY%)
  44.     lastX! = nx!
  45.     lastY! = ny!
  49.  

Leaves
Code: QB64: [Select]
  1. 'Original IFS fractal by Andy Amaya
  2. 'ap3-180130-095
  3. _TITLE "IFS Nice Leaves"
  4.  
  5. scale! = 148.7642
  6. offsetX% = 391
  7. offsetY% = 203
  8. SCREEN _NEWIMAGE(800, 600, 32)
  9. CLS , _RGB32(32, 0, 8)
  10. COLOR _RGB32(0, 192, 0, 48)
  11.  
  12. FOR iter& = 0 TO 1000000
  14.         CASE 0 TO .36
  15.             nx! = .490662 * lastX! + .357636 * lastY! + .992214
  16.             ny! = -.367636 * lastX! + .490662 * lastY! + -.032411
  17.         CASE .37 TO .99
  18.             nx! = -.1878 * lastX! + -.893171 * lastY! + -.283457
  19.             ny! = -.67173 * lastX! + .196847 * lastY! + .612409
  20.         CASE ELSE
  21.             nx! = -.222345 * lastX! + -.170637 * lastY! + .900462
  22.             ny! = .129271 * lastX! + .118929 * lastY! + -.778578
  23.     END SELECT
  24.     IF iter& > 20& THEN PSET (nx! * scale! + offsetX%, ny! * scale! + offsetY%)
  25.     lastX! = nx!
  26.     lastY! = ny!

More Leaves
Code: QB64: [Select]
  1. 'Original IFS fractal by Andy Amaya
  2. 'ap3--180220-341
  3. _TITLE "IFS More Leaves"
  4.  
  5. scale! = 177.136
  6. offsetX% = 676
  7. offsetY% = 133
  8. SCREEN _NEWIMAGE(800, 600, 32)
  9. CLS , _RGB32(8, 8, 64)
  10. COLOR _RGB32(16, 224, 16, 32)
  11.  
  12. FOR iter& = 0 TO 1000000
  14.         CASE 0 TO .500
  15.             nx! = .161173 * lastX! + -.705634 * lastY! + -.881538
  16.             ny! = -.705634 * lastX! + -.161173 * lastY! + .717868
  17.         CASE .501 TO .990
  18.             nx! = .579204 * lastX! + -.271884 * lastY! + -.129897
  19.             ny! = .271884 * lastX! + .579204 * lastY! + .028496
  20.         CASE ELSE
  21.             nx! = -.286384 * lastX! + -.337266 * lastY! + -.490174
  22.             ny! = .223508 * lastX! + .280943 * lastY! + .382861
  23.     END SELECT
  24.     IF iter& > 20& THEN PSET (nx! * scale! + offsetX%, ny! * scale! + offsetY%)
  25.     lastX! = nx!
  26.     lastY! = ny!




« Last Edit: December 09, 2019, 12:36:19 am by AndyA »
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Offline bplus

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Re: Original IFS Fractals
« Reply #1 on: December 09, 2019, 11:06:50 am »
Hi Andy,

Very nice! amazing what a little bit of code can produce! Not only super fast, they seem super small compared to SDL as I remember, what? 3 years ago??

Say, do you have any pine trees?

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Offline Petr

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Re: Original IFS Fractals
« Reply #2 on: December 09, 2019, 04:06:43 pm »
Very nice!
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Offline AndyA

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Re: Original IFS Fractals
« Reply #3 on: December 09, 2019, 07:01:29 pm »
Thanks guys!

@bplus

The codes are much shorter because I don't have to :
1) Create a lookup table for alpha-drawing the fractal, just set the alpha level and let QB64 do it's stuff.
2) Don't have to create a histogram array to speed up the rendering process, once again QB64 is plenty fast. Being a compiled language that's not a big surprise.

Long term, I'm going to have to figure out how to work with Inform. Inform seems to be based on VB like code SUBs, where you design the form (UI) which generates the event SUBs, then fill in the SUBs and logic glue code. Very slick! Then I can recreate the fast BlitzPlus Basic IFS Viewer program in QB64.

As for pine trees (Christmas card/demo anyone?), I should be able to find or make a few for you. I'll try to hook you up in the next couple of days (work schedule permitting).



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FellippeHeitor

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Re: Original IFS Fractals
« Reply #4 on: December 09, 2019, 07:05:20 pm »
Quote from: AndyA on December 09, 2019, 07:01:29 pm
Long term, I'm going to have to figure out how to work with Inform. Inform seems to be based on VB like code SUBs, where you design the form (UI) which generates the event SUBs, then fill in the SUBs and logic glue code. Very slick! Then I can recreate the fast BlitzPlus Basic IFS Viewer program in QB64.

Let me know if you need any assistance with InForm ❤️
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Offline AndyA

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Re: Original IFS Fractals
« Reply #5 on: December 09, 2019, 09:41:05 pm »
Thanks for the encouragement Fellippe!  I may have to take you up on that :)

@bplus

It's kinda lopsided, but may be able to tweak to achieve symmetry.

Pine Tree
Code: QB64: [Select]
  1. 'Original IFS fractal by Andy Amaya
  2. 'ap3-191209-216
  3. _TITLE "IFS Pine Tree"
  4.  
  5. scaleX! = 524.0 '424.0 to 1024.0 look OK for X scaling factor
  6. scaleY! = 524.0
  7. offsetX% = 370
  8. offsetY% = 150
  9. SCREEN _NEWIMAGE(800, 600, 32)
  10. CLS , _RGB32(0, 0, 0)
  11. COLOR _RGB32(0, 228, 0, 24)
  12.  
  13. FOR iter& = 0 TO 1000000
  15.         CASE 0 TO .62
  16.             nx! = -0.858985 * lastX! + 0.008944 * lastY! + 0.092336
  17.             ny! = 0.012263 * lastX! + 0.84816 * lastY! + -0.04103
  18.         CASE .63 TO .98
  19.             nx! = -0.373759 * lastX! + -0.353068 * lastY! + 0.296535
  20.             ny! = 0.353068 * lastX! + -0.373759 * lastY! + 0.704598
  21.         CASE ELSE
  22.             nx! = 0.010276 * lastX! + 0 * lastY! + 0.053328
  23.             ny! = -0.05138 * lastX! + 0.313416 * lastY! + 0.576552
  24.     END SELECT
  25.     IF iter& > 20& THEN PSET (nx! * scaleX! + offsetX%, ny! * scaleY! + offsetY%)
  26.     lastX! = nx!
  27.     lastY! = ny!
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Offline bplus

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Re: Original IFS Fractals
« Reply #6 on: December 09, 2019, 11:05:42 pm »
Hey not bad, thanks Andy!
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Offline Ashish

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Re: Original IFS Fractals
« Reply #7 on: December 14, 2019, 11:16:00 pm »
Amazing! I have never seen these before. Indeed, they all are original.
How you make this? I mean what you do for making new fractal?
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Offline johnno56

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Re: Original IFS Fractals
« Reply #8 on: December 15, 2019, 04:24:13 pm »
Cool... The only things missing are the scent of pine and the squeaking of squirrels... Nicely done!
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Offline AndyA

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Re: Original IFS Fractals
« Reply #9 on: December 16, 2019, 12:05:57 am »
@Ashish
The first post has the links to the programs I use for designing the IFS Fractals. When using Apophysis, just remember to turn off the 'flame fractal' settings by unchecking all of the different types of effects (e.g. sinusoidal, spherical, swirl, horse shoe, etc.).

To do this, do the following:
1) Fire up Apophysis
2) Select 'Options' menu from the menu bar at the top
3) Select 'Options P' at the bottom of the drop down menu
4) This brings up an 'Options' dialog box.
5) Select the 'Clear All' button at the bottom right
6) Click the 'linear' checkbox at the top left (make sure linear is the only option left checked).
7) Click the 'OK' button.

Done. Now select one of the IFS fractal previews on the far left.  Press 'F4' and start messing with the triangles.

If you design something you like, save as an .IFS, not as a flame fractal.

@Johnno56
Thanks!  I hope these run a lot better than the others I did in SDL Basic, i.e. no run time errors for Linux users.
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