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Active Forums => Programs => Topic started by: AndyA on February 20, 2021, 01:51:56 am

Title: A dozen new and original IFS fractals
Post by: AndyA on February 20, 2021, 01:51:56 am
I was playing with Apophysis (a fractal generator with design editing, which is what I've been using) and came up with these (all except Spiral Tunnel).

I made these so that they should fit on a 1366 x 768 screen. That's what I had for a few years. If it doesn't quite fit, just change the screen height to 750 or even 745, that should do the trick.

Three of these are just variations on the same theme, namely 'Pointy Star', 'Star Wings' and 'Fluffy Star'. Just small changes create quite different images.


This one I like because of the detail of nested self-similar spirals.
Braided Spirals
Code: QB64: [Select]
  1. 'Original IFS fractal by Andy Amaya
  2. 'Braided Spirals
  3. _TITLE "IFS Braided Spirals"
  4.  
  5. SCREEN _NEWIMAGE(1024, 755, 32)
  7.  
  8. scale! = 542.543
  9. offsetX% = 280
  10. offsetY% = 412
  11.  
  12. gradient% = 1
  13. IF gradient% = 1 THEN
  14.     red! = 160.0
  15.     grn! = 0.0
  16.     blu! = 0.0
  17.  
  18.     COLOR _RGB(red!, grn!, blu!)
  19.     FOR i = 0 TO 755 STEP 3
  20.         LINE (0, i)-(1023, i + 2), , BF
  21.         red! = red! - .4
  22.         COLOR _RGB(red!, grn!, blu!)
  23.     NEXT
  25.     CLS , _RGB32(80, 0, 0)
  27.  
  28. COLOR _RGB32(255, 255, 255, 60)
  29. FOR iter& = 0 TO 1500000
  31.         CASE 0 TO 0.84
  32.             nx! = -0.940076 * lastX! + 0.109322 * lastY! + 0.868750
  33.             ny! = -0.132901 * lastX! + -0.959883 * lastY! + -0.061005
  34.         CASE 0.8400001 TO 0.93
  35.             nx! = -0.200339 * lastX! + -0.070879 * lastY! + 0.082227
  36.             ny! = 0.119883 * lastX! + -0.250145 * lastY! + 0.019925
  37.         CASE ELSE
  38.             nx! = 0.059150 * lastX! + -0.264528 * lastY! + -0.375950
  39.             ny! = 0.197019 * lastX! + -0.015262 * lastY! + 0.178505
  40.     END SELECT
  41.     IF iter& > 20& THEN PSET (nx! * scale! + offsetX%, ny! * scale! + offsetY%)
  42.     lastX! = nx!
  43.     lastY! = ny!
  47.  

IFS Dande-Leaf
Code: QB64: [Select]
  1. 'Original IFS fractal by Andy Amaya
  2. 'Dande-Leaf
  3. _TITLE "IFS Dande-Leaf"
  4.  
  5. SCREEN _NEWIMAGE(1024, 755, 32)
  7. CLS , _RGB32(0, 0, 80)
  8.  
  9. scale! = 124.552
  10.  
  11. transpose = 1
  12. IF transpose = 0 THEN
  13.     'Plot in usual way
  14.     offsetX% = 445: offsetY% = 201
  16.     'flip the X and Y axis to turn the graphic 90 degrees
  17.     offsetX% = 301: offsetY% = 251
  19.  
  20. red! = 128.0
  21. grn! = 128.0
  22. blu! = 0.0
  23.  
  24. COLOR _RGB(red!, grn!, blu!)
  25. FOR i = 0 TO 755 STEP 3
  26.     LINE (0, i)-(1023, i + 2), , BF
  27.     red! = red! - 0.4
  28.     grn! = grn! - 0.4
  29.     COLOR _RGB(red!, grn!, blu!)
  31.  
  32. COLOR _RGB32(255, 255, 255, 48)
  33. FOR iter& = 0 TO 1000000
  35.         CASE 0 TO 0.67
  36.             nx! = -0.843080 * lastX! + 0.508739 * lastY! + 0.366725
  37.             ny! = 0.508739 * lastX! + 0.843080 * lastY! + 0.305420
  38.         CASE 0.6700001 TO 0.97
  39.             nx! = 0.626559 * lastX! + -0.250481 * lastY! + -0.212725
  40.             ny! = 0.294432 * lastX! + 0.482080 * lastY! + 0.090219
  41.         CASE ELSE
  42.             nx! = -0.052541 * lastX! + -0.028642 * lastY! + -0.041935
  43.             ny! = -0.125541 * lastX! + -0.110988 * lastY! + -0.679700
  44.     END SELECT
  45.     IF transpose = 0 THEN
  46.         IF iter& > 20& THEN PSET (nx! * scale! + offsetX%, ny! * scale! + offsetY%)
  47.     ELSE
  48.         IF iter& > 20& THEN PSET (ny! * scale! + offsetY%, nx! * scale! + offsetX%)
  49.     END IF
  50.     lastX! = nx!
  51.     lastY! = ny!

IFS Dry Leaves
Code: QB64: [Select]
  1. 'Original IFS fractal by Andy Amaya
  2. 'Dry Leaves
  3. _TITLE "IFS Dry Leaves"
  4.  
  5. SCREEN _NEWIMAGE(1024, 755, 32)
  7.  
  8. scale! = 324.140
  9. offsetX% = 570
  10. offsetY% = 297
  11.  
  12. gradient% = 1
  13. IF gradient% = 1 THEN
  14.     red! = 255.0
  15.     grn! = 255.0
  16.     blu! = 255.0
  17.     COLOR _RGB(red!, grn!, blu!)
  18.     FOR i = 0 TO 755 STEP 3
  19.         LINE (0, i)-(1023, i + 2), , BF
  20.         red! = red! - .9
  21.         grn! = grn! - .9
  22.         blu! = blu! - .8
  23.         COLOR _RGB(red!, grn!, blu!)
  24.     NEXT
  26.     CLS , _RGB32(112, 112, 128)
  28.  
  29. COLOR _RGB32(80, 48, 0, 60)
  30. FOR iter& = 0 TO 1500000
  32.         CASE 0 TO 0.44
  33.             nx! = -0.243869 * lastX! + -0.745420 * lastY! + -0.003990
  34.             ny! = -0.745420 * lastX! + 0.243869 * lastY! + 0.425844
  35.         CASE 0.4400001 TO 0.82
  36.             nx! = 0.398172 * lastX! + -0.533236 * lastY! + -0.111045
  37.             ny! = -0.564692 * lastX! + -0.362100 * lastY! + -0.200485
  38.         CASE ELSE
  39.             nx! = -0.139673 * lastX! + -0.110775 * lastY! + 0.406389
  40.             ny! = 0.178204 * lastX! + 0.157489 * lastY! + -0.319936
  41.     END SELECT
  42.     IF iter& > 20& THEN PSET (nx! * scale! + offsetX%, ny! * scale! + offsetY%)
  43.     lastX! = nx!
  44.     lastY! = ny!

IFS Fire Leaves
Code: QB64: [Select]
  1. 'Original IFS fractal by Andy Amaya
  2. 'Fire Leaves
  3. _TITLE "IFS Fire Leaves"
  4.  
  5. SCREEN _NEWIMAGE(1024, 755, 32)
  7.  
  8. scale! = 323.610
  9. offsetX% = 240
  10. offsetY% = 305
  11.  
  12. gradient% = 1
  13. IF gradient% = 1 THEN
  14.     red! = 0.0
  15.     grn! = 128.0
  16.     blu! = 0.0
  17.     COLOR _RGB(red!, grn!, blu!)
  18.     FOR i = 0 TO 755 STEP 3
  19.         LINE (0, i)-(1023, i + 2), , BF
  20.         'red! = red! - .4
  21.         grn! = grn! - .4
  22.         blu! = blu! + .4
  23.         COLOR _RGB(red!, grn!, blu!)
  24.     NEXT
  26.     CLS , _RGB32(0, 0, 64)
  28.  
  29. COLOR _RGB32(255, 96, 0, 60)
  30. FOR iter& = 0 TO 1500000
  32.         CASE 0 TO 0.55
  33.             nx! = 0.450145 * lastX! + -0.725674 * lastY! + 0.850926
  34.             ny! = -0.772767 * lastX! + -0.295871 * lastY! + 0.943063
  35.         CASE 0.550001 TO 0.98
  36.             nx! = -0.125597 * lastX! + -0.569436 * lastY! + 0.336491
  37.             ny! = -0.435385 * lastX! + 0.435182 * lastY! + 0.274180
  38.         CASE ELSE
  39.             nx! = -0.132432 * lastX! + -0.278862 * lastY! + -0.051857
  40.             ny! = 0.077123 * lastX! + 0.171443 * lastY! + 0.884371
  41.     END SELECT
  42.     IF iter& > 20& THEN PSET (nx! * scale! + offsetX%, ny! * scale! + offsetY%)
  43.     lastX! = nx!
  44.     lastY! = ny!

IFS Fluffy Star
Code: QB64: [Select]
  1. 'Original IFS fractal by Andy Amaya
  2. 'Fluffy Star
  3. _TITLE "IFS Fluffy Star"
  4.  
  5. SCREEN _NEWIMAGE(1024, 755, 32)
  7.  
  8. scale! = 324.349
  9. offsetX% = 504
  10. offsetY% = 401
  11.  
  12. gradient% = 1
  13. IF gradient% = 1 THEN
  14.     red! = 0.0
  15.     grn! = 0.0
  16.     blu! = 128.0
  17.     COLOR _RGB(red!, grn!, blu!)
  18.     FOR i = 0 TO 755 STEP 3
  19.         LINE (0, i)-(1023, i + 2), , BF
  20.         blu! = blu! - .4
  21.         COLOR _RGB(red!, grn!, blu!)
  22.     NEXT
  24.     CLS , _RGB32(0, 0, 64)
  26.  
  27. COLOR _RGB32(208, 208, 255, 48)
  28. FOR iter& = 0 TO 1500000
  30.         CASE 0 TO 0.782261
  31.             nx! = -0.816914 * lastX! + 0.561746 * lastY! + -0.003345
  32.             ny! = -0.561746 * lastX! + -0.816914 * lastY! + 0.002228
  33.         CASE ELSE
  34.             nx! = 0.282758 * lastX! + 0.390905 * lastY! + -0.636573
  35.             ny! = 0.010828 * lastX! + 0.310650 * lastY! + -0.176126
  36.     END SELECT
  37.     IF iter& > 20& THEN PSET (nx! * scale! + offsetX%, ny! * scale! + offsetY%)
  38.     lastX! = nx!
  39.     lastY! = ny!

IFS Lined Spiral
Code: QB64: [Select]
  1. 'Original IFS fractal by Andy Amaya
  2. 'Lined Spiral
  3. _TITLE "IFS Lined Spiral"
  4.  
  5. SCREEN _NEWIMAGE(1024, 755, 32)
  7.  
  8. scale! = 511.730
  9. offsetX% = 309
  10. offsetY% = 102
  11.  
  12. gradient% = 1
  13. IF gradient% = 1 THEN
  14.     red! = 128.0
  15.     grn! = 0.0
  16.     blu! = 0.0
  17.  
  18.     COLOR _RGB(red!, grn!, blu!)
  19.     FOR i = 0 TO 755 STEP 3
  20.         LINE (0, i)-(1023, i + 2), , BF
  21.         red! = red! - .44
  22.         blu! = blu! + .88
  23.         COLOR _RGB(red!, grn!, blu!)
  24.     NEXT
  26.     CLS , _RGB32(24, 16, 0)
  28. COLOR _RGB32(255, 255, 255, 60)
  29.  
  30. FOR iter& = 0 TO 1500000
  32.         CASE 0 TO 0.85
  33.             nx! = 0.831291 * lastX! + 0.404627 * lastY! + -0.054528
  34.             ny! = -0.404627 * lastX! + 0.831291 * lastY! + 0.327965
  35.         CASE 0.8500001 TO 0.99
  36.             nx! = 0.206141 * lastX! + 0.202595 * lastY! + -0.427254
  37.             ny! = -0.202595 * lastX! + 0.206141 * lastY! + 0.093335
  38.         CASE ELSE
  39.             nx! = -0.065637 * lastX! + -0.060614 * lastY! + 0.174141
  40.             ny! = 0.112378 * lastX! + 0.115166 * lastY! + -0.124196
  41.     END SELECT
  42.     IF iter& > 20& THEN PSET (nx! * scale! + offsetX%, ny! * scale! + offsetY%)
  43.     lastX! = nx!
  44.     lastY! = ny!

IFS Oak Leaves
Code: QB64: [Select]
  1. 'Original IFS fractal by Andy Amaya
  2. 'Oak Leaves
  3. _TITLE "IFS Oak Leaves"
  4.  
  5. SCREEN _NEWIMAGE(1024, 755, 32)
  7.  
  8. scale! = 324.140
  9. offsetX% = 570
  10. offsetY% = 297
  11.  
  12. gradient% = 1
  13. IF gradient% = 1 THEN
  14.     red! = 96.0
  15.     grn! = 0.0
  16.     blu! = 192.0
  17.     COLOR _RGB(red!, grn!, blu!)
  18.     FOR i = 0 TO 755 STEP 3
  19.         LINE (0, i)-(1023, i + 2), , BF
  20.         red! = red! - .4
  21.         blu! = blu! - .7
  22.         COLOR _RGB(red!, grn!, blu!)
  23.     NEXT
  25.     CLS , _RGB32(64, 0, 128)
  27.  
  28. COLOR _RGB32(64, 255, 32, 60)
  29. FOR iter& = 0 TO 1500000
  31.         CASE 0 TO 0.58
  32.             nx! = -0.243869 * lastX! + -0.745420 * lastY! + -0.003990
  33.             ny! = -0.745420 * lastX! + 0.243869 * lastY! + 0.425844
  34.         CASE 0.5800001 TO 0.99
  35.             nx! = 0.398172 * lastX! + -0.533236 * lastY! + -0.122126
  36.             ny! = -0.564692 * lastX! + -0.362100 * lastY! + -0.184116
  37.         CASE ELSE
  38.             nx! = -0.139673 * lastX! + -0.110775 * lastY! + 0.406389
  39.             ny! = 0.178204 * lastX! + 0.154489 * lastY! + -0.319936
  40.     END SELECT
  41.     IF iter& > 20& THEN PSET (nx! * scale! + offsetX%, ny! * scale! + offsetY%)
  42.     lastX! = nx!
  43.     lastY! = ny!

IFS Pinwheel
Code: QB64: [Select]
  1. 'Original IFS fractal by Andy Amaya
  2. 'Pinwheel
  3. _TITLE "IFS Pinwheel"
  4.  
  5. scale! = 253.200
  6. offsetX% = 385
  7. offsetY% = 428
  8. SCREEN _NEWIMAGE(1024, 755, 32)
  10. CLS , _RGB32(0, 0, 80)
  11.  
  12.  
  13. blu! = 255.0
  14. COLOR _RGB(0, 0, blu!)
  15.  
  16. FOR i = 0 TO 755 STEP 3
  17.     LINE (0, i)-(1023, i + 2), , BF
  18.     blu! = blu! - 0.85
  19.     COLOR _RGB(0, 0, blu!)
  21.  
  22. COLOR _RGB32(255, 255, 96, 48)
  23. FOR iter& = 0 TO 2000000
  25.         CASE 0 TO .8
  26.             nx! = 0.004855 * lastX! + -0.990169 * lastY! + 0.333507
  27.             ny! = 0.990169 * lastX! + 0.004855 * lastY! + -0.690207
  28.         CASE ELSE
  29.             nx! = 0.143532 * lastX! + 0.552904 * lastY! + -0.165432
  30.             ny! = -0.266752 * lastX! + 0.203483 * lastY! + 0.086279
  31.     END SELECT
  32.     IF iter& > 20& THEN PSET (nx! * scale! + offsetX%, ny! * scale! + offsetY%)
  33.     lastX! = nx!
  34.     lastY! = ny!

IFS Pointy Star
Code: QB64: [Select]
  1. 'Original IFS fractal by Andy Amaya
  2. 'Pointy Star
  3. _TITLE "IFS Pointy Star"
  4.  
  5. SCREEN _NEWIMAGE(1024, 755, 32)
  6.  
  7. scale! = 270.0
  8. offsetX% = 509
  9. offsetY% = 376
  10.  
  11. gradient% = 1
  12. IF gradient% = 1 THEN
  13.     red! = 0.0
  14.     grn! = 0.0
  15.     blu! = 128.0
  16.     COLOR _RGB(red!, grn!, blu!)
  17.     FOR i = 0 TO 755 STEP 3
  18.         LINE (0, i)-(1023, i + 2), , BF
  19.         blu! = blu! - .4
  20.         COLOR _RGB(red!, grn!, blu!)
  21.     NEXT
  23.     CLS , _RGB32(0, 0, 64)
  25.  
  26. COLOR _RGB32(208, 208, 255, 48)
  27. FOR iter& = 0 TO 1500000
  29.         CASE 0 TO 0.782261
  30.             nx! = -0.814831 * lastX! + 0.574685 * lastY! + -0.003345
  31.             ny! = -0.564763 * lastX! + -0.741019 * lastY! + 0.002228
  32.         CASE ELSE
  33.             nx! = 0.364791 * lastX! + 0.278183 * lastY! + -0.630902
  34.             ny! = 0.221807 * lastX! + 0.418540 * lastY! + -0.204482
  35.     END SELECT
  36.     IF iter& > 20& THEN PSET (nx! * scale! + offsetX%, ny! * scale! + offsetY%)
  37.     lastX! = nx!
  38.     lastY! = ny!

This one is an old one, but I'm a sucker for spiral variations.

IFS Spiral Tunnel   (generated by J.C. Sprott - IFS.bas)
Code: QB64: [Select]
  1. 'Original IFS fractal by Andy Amaya
  2. 'Spiral Tunnel
  3. _TITLE "IFS Spiral Tunnel"
  4.  
  5. scaleX! = 709.466
  6. scaleY! = 380.466
  7. offsetX% = 367
  8. offsetY% = 327
  9. SCREEN _NEWIMAGE(1024, 755, 32)
  11.  
  12. red! = 255.0
  13. grn! = 255.0
  14. blu! = 0.0
  15. COLOR _RGB(red!, grn!, blu!)
  16.  
  17. FOR i = 0 TO 755 STEP 3
  18.     LINE (0, i)-(1023, i + 2), , BF
  19.     red! = red! - 0.85
  20.     grn! = grn! - 0.95
  21.     COLOR _RGB(red!, grn!, blu!)
  23.  
  24. COLOR _RGB32(64, 0, 160, 48)
  25. FOR iter& = 0 TO 2000000
  27.         CASE 0 TO .833
  28.             nx! = -0.70 * lastX! + 0.30 * lastY! + 0.30
  29.             ny! = -0.90 * lastX! + -0.80 * lastY! + 0.50
  30.         CASE ELSE
  31.             nx! = -0.20 * lastX! + 0.30 * lastY! + -0.10
  32.             ny! = 0.90 * lastX! + -0.80 * lastY! + 0.00
  33.     END SELECT
  34.     IF iter& > 20& THEN PSET (nx! * scaleX! + offsetX%, ny! * scaleY! + offsetY%)
  35.     lastX! = nx!
  36.     lastY! = ny!

IFS Star Wings
Code: QB64: [Select]
  1. 'Original IFS fractal by Andy Amaya
  2. 'Star Wings
  3. _TITLE "IFS Star Wings"
  4.  
  5. SCREEN _NEWIMAGE(1024, 755, 32)
  7.  
  8. scale! = 324.349
  9. offsetX% = 504
  10. offsetY% = 401
  11.  
  12. gradient% = 1
  13. IF gradient% = 1 THEN
  14.     red! = 0.0
  15.     grn! = 0.0
  16.     blu! = 128.0
  17.     COLOR _RGB(red!, grn!, blu!)
  18.     FOR i = 0 TO 755 STEP 3
  19.         LINE (0, i)-(1023, i + 2), , BF
  20.         blu! = blu! - .4
  21.         COLOR _RGB(red!, grn!, blu!)
  22.     NEXT
  24.     CLS , _RGB32(0, 0, 64)
  26.  
  27. COLOR _RGB32(208, 208, 255, 48)
  28. FOR iter& = 0 TO 1500000
  30.         CASE 0 TO 0.782261
  31.             nx! = -0.816914 * lastX! + 0.561746 * lastY! + -0.003345
  32.             ny! = -0.561746 * lastX! + -0.816914 * lastY! + 0.002228
  33.         CASE ELSE
  34.             nx! = 0.282758 * lastX! + 0.390905 * lastY! + -0.636573
  35.             ny! = 0.010828 * lastX! + 0.310650 * lastY! + -0.176126
  36.     END SELECT
  37.     IF iter& > 20& THEN PSET (nx! * scale! + offsetX%, ny! * scale! + offsetY%)
  38.     lastX! = nx!
  39.     lastY! = ny!


This one reminded me of those creatures from the movie 'Tremors'.

IFS Tricera-Fract
Code: QB64: [Select]
  1. 'Original IFS fractal by Andy Amaya
  2. 'Tricera-Fract
  3. _TITLE "IFS Tricera-Fract"
  4.  
  5. SCREEN _NEWIMAGE(1024, 755, 32)
  7.  
  8. scale! = 264.736
  9. offsetX% = 630
  10. offsetY% = 425
  11.  
  12. gradient% = 1
  13. IF gradient% = 1 THEN
  14.     red! = 62.0
  15.     grn! = 31.0
  16.     blu! = 0.0
  17.  
  18.     COLOR _RGB(red!, grn!, blu!)
  19.     FOR i = 0 TO 755 STEP 3
  20.         LINE (0, i)-(1023, i + 2), , BF
  21.         red! = red! - .22
  22.         grn! = grn! - .12
  23.         COLOR _RGB(red!, grn!, blu!)
  24.     NEXT
  26.     CLS , _RGB32(24, 16, 0)
  28. COLOR _RGB32(255, 255, 180, 60)
  29.  
  30. FOR iter& = 0 TO 1500000
  32.         CASE 0 TO 0.62
  33.             nx! = -0.516076 * lastX! + -0.792133 * lastY! + -0.542779
  34.             ny! = 0.792133 * lastX! + -0.516076 * lastY! + 0.412808
  35.         CASE 0.6200001 TO 0.84
  36.             nx! = 0.294921 * lastX! + 0.240110 * lastY! + 0.493068
  37.             ny! = -0.032464 * lastX! + 0.345342 * lastY! + 0.808644
  38.         CASE ELSE
  39.             nx! = -0.170761 * lastX! + -0.276078 * lastY! + -0.229303
  40.             ny! = 0.265610 * lastX! + -0.179727 * lastY! + -0.375222
  41.     END SELECT
  42.     IF iter& > 20& THEN PSET (nx! * scale! + offsetX%, ny! * scale! + offsetY%)
  43.     lastX! = nx!
  44.     lastY! = ny!
Title: Re: A dozen new and original IFS fractals
Post by: bplus on February 20, 2021, 02:12:57 am
Very nice! I think you've been working on background colorings, fire leaf definitely struck me with color usage, and some of fractals look they are being rotated in 3D. Beautiful works of art all!

Oh also they are rendered almost immediately.

After Screen _NewImage....
_delay .25
_ScreenMove _middle ' to center
Title: Re: A dozen new and original IFS fractals
Post by: bplus on February 20, 2021, 02:24:21 am
Reversed Green and Blue:
 


Code: QB64: [Select]
  1.  'Original IFS fractal by Andy Amaya
  2. 'Fire Leaves
  3. _TITLE "IFS Fire Leaves"
  4.  
  5. SCREEN _NEWIMAGE(1024, 755, 32)
  6. _DELAY .25
  8.  
  10.  
  11. scale! = 323.610
  12. offsetX% = 240
  13. offsetY% = 305
  14.  
  15. gradient% = 1
  16. IF gradient% = 1 THEN
  17.     red! = 0.0
  18.     grn! = 0
  19.     blu! = 128
  20.     COLOR _RGB(red!, grn!, blu!)
  21.     FOR i = 0 TO 755 STEP 3
  22.         LINE (0, i)-(1023, i + 2), , BF
  23.         'red! = red! - .4
  24.         grn! = grn! + .4
  25.         blu! = blu! - .4
  26.         COLOR _RGB(red!, grn!, blu!)
  27.     NEXT
  29.     CLS , _RGB32(0, 0, 64)
  31.  
  32. COLOR _RGB32(255, 96, 0, 60)
  33. FOR iter& = 0 TO 1500000
  35.         CASE 0 TO 0.55
  36.             nx! = 0.450145 * lastX! + -0.725674 * lastY! + 0.850926
  37.             ny! = -0.772767 * lastX! + -0.295871 * lastY! + 0.943063
  38.         CASE 0.550001 TO 0.98
  39.             nx! = -0.125597 * lastX! + -0.569436 * lastY! + 0.336491
  40.             ny! = -0.435385 * lastX! + 0.435182 * lastY! + 0.274180
  41.         CASE ELSE
  42.             nx! = -0.132432 * lastX! + -0.278862 * lastY! + -0.051857
  43.             ny! = 0.077123 * lastX! + 0.171443 * lastY! + 0.884371
  44.     END SELECT
  45.     IF iter& > 20& THEN PSET (nx! * scale! + offsetX%, ny! * scale! + offsetY%)
  46.     lastX! = nx!
  47.     lastY! = ny!
Title: Re: A dozen new and original IFS fractals
Post by: Dav on February 20, 2021, 06:39:47 am
These are absolutely beautiful.  Well deserving of obtaining a special folder in my qb64 directory.  Thanks for sharing!

- Dav
Title: Re: A dozen new and original IFS fractals
Post by: bplus on February 20, 2021, 09:53:14 am
I am looking at Fire Leaves again and thinking one can render a fire effect faster maybe if:

1. Don't start drawing the sticky parts until the level is reached they dont look like sticks,
2. Alter the color red with fire pallet or palette, oh color by recurs level the lower levels white and yellow really low a dash of blue!
3. Overlap several renderings
4. Point the first sticks up

maybe? well maybe for a still shot.
Title: Re: A dozen new and original IFS fractals
Post by: bplus on February 20, 2021, 09:59:50 am
Oh! To see the Beast run this in Roto and rotate 40 degrees +/-

 



The Beast has a Vortex for mouth and nose that sucks in star systems or you! like a vacuum cleaner, it is most anti-anti-gravity.


Oh heck run this in rotozoom with cls by fades.
Title: Re: A dozen new and original IFS fractals
Post by: AndyA on February 20, 2021, 11:34:14 am
Thanks for the kind words.

@Dav
I did some other IFS fractals on this post: https://www.qb64.org/forum/index.php?topic=1965.0

Ashish has also done some IFS fractals and L-System fractals.

Someone else did some fractals converted from 'Ultra Fractal' or something similar.

Just goes to show what can be done mathematically to draw images.


@bplus
I like the reversal of the background in 'Fire Leaves' that you did, it somehow looks better, even though the color palette is the same.

As for 'Fire Leaves' (and all the others for that matter), the image is drawn one point at a random location in the 'orbit' of the 'attractor'. This boils down to, there's no way to procedurally draw anything, it's always going to be a single point drawn at a random location in the image.
Title: Re: A dozen new and original IFS fractals
Post by: bplus on February 20, 2021, 11:48:35 am
Quote
This boils down to, there's no way to procedurally draw anything, it's always going to be a single point drawn at a random location in the image.

I managed to draw the classic fern and your pine tree any where on screen with different palettes, did you see Christmas 2020? ;-))

Reply #17 Christmas 2020 Thread
https://www.qb64.org/forum/index.php?topic=3332.msg126398#msg126398

These snippets have a center x, y they are drawn albeit randomly but you can rubber stamp process and alter colors and scales... even sway the ferns in the wind!
Code: QB64: [Select]
  1. _TITLE "Fernerator, press spacebar for new landscape, esc to quit" 'b+ 2020-08-06
  2. SCREEN _NEWIMAGE(1000, 600, 32)
  3. _DELAY .25
  5. WINDOW (-5, 0)-(5, 11)
  7.  
  8. TYPE obj
  9.     x AS SINGLE 'offset from centered fern
  10.     y AS SINGLE 'offest from centered fern
  11.     scale AS SINGLE ' from 0 to 1
  12.     c AS _UNSIGNED LONG
  14.  
  15. DIM SHARED nFerns
  16. REDIM SHARED fern(1 TO nFerns) AS obj
  17. '   f& = _LOADIMAGE("clipartkey_1043733.png")  ' the code isn't working with the image anymore???
  18.  
  19. initFerns
  20. wind = 0: dw = .01: dir = 1
  21. WHILE _KEYDOWN(27) = 0
  22.     IF INKEY$ = " " THEN initFerns
  23.     FOR i = 4 TO 11 STEP .2
  24.         LINE (-5, i)-(5, i + .2), _RGB32(60, (1 - i / 11) * 150 + 60, (1 - i / 11) * 75 + 180), BF
  25.     NEXT
  26.     FOR i = 0 TO 4 STEP .2
  27.         LINE (-5, i)-(5, i + .2), _RGB32(i / 4 * 90 + 10, i / 4 * 45 + 5, i / 4 * 22 + 2), BF
  28.     NEXT
  29.     ''''''''''''''''''''''''''''''''''''''''''''_PUTIMAGE (-5, 0), f&, 0 ' the code isn't working with the image anymore???
  30.  
  31.     FOR i = 1 TO nFerns
  32.         drawFern fern(i).x, fern(i).y, fern(i).scale, fern(i).c, wind
  33.     NEXT
  34.  
  35.     _DISPLAY
  36.     _LIMIT 10
  37.     wind = wind + dir * dw
  38.     IF wind > .06 OR wind < -.72 THEN dir = -dir
  40.  
  41. SUB initFerns
  42.     nFerns = 4 + INT(RND * 9)
  43.     REDIM fern(1 TO nFerns) AS obj
  44.     FOR i = 1 TO nFerns
  45.         fern(i).x = RND * 10 - 5
  46.         fern(i).y = RND * 2 - 1
  47.         fern(i).scale = RND * .7 + .3
  48.         g = RND * 100 + 40
  49.         fern(i).c = _RGB32(g - 20 - RND * 60, g, g - 20 - RND * 60)
  50.     NEXT
  52.  
  53. SUB drawFern (xoff0, yoff0, scale, c AS _UNSIGNED LONG, w)
  54.     yAdj = yoff0 + (1 - scale) * 5
  55.     FOR i = 1 TO 90000 'enough dots to get idea
  56.         SELECT CASE RND
  57.             CASE IS < .01
  58.                 nextX = 0
  59.                 nextY = .16 * y
  60.             CASE .01 TO .08
  61.                 nextX = .2 * x - .26 * y
  62.                 nextY = .23 * x + .22 * y + 1.6
  63.             CASE .08 TO .15
  64.                 nextX = -.15 * x + .28 * y
  65.                 nextY = .26 * x + .24 * y + .44
  66.             CASE ELSE
  67.                 nextX = .85 * x + .04 * y
  68.                 nextY = -.04 * x + .85 * y + 1.6
  69.         END SELECT
  70.         x = nextX + w * nextY / 10
  71.         y = nextY
  72.         LINE (x * scale + xoff0, y * scale + yAdj)-STEP(0, 0), c, BF
  73.     NEXT
  75.  
  76.  

EDIT: the code isn't working right with image any more, dang!

Also could alter the images my alternating the random rendering of x, y points so ferns dont look so cloned.
 
Title: Re: A dozen new and original IFS fractals
Post by: AndyA on February 20, 2021, 02:39:55 pm
Those are clever changes to the plotting and post-rendering of the images, but I prefer using images for post processing the IFS like the attached pic. Using images for post processing allows me more flexibility in making a more realistic IFS picture. It's not everybody's cup of tea but I like it just fine.
Title: Re: A dozen new and original IFS fractals
Post by: bplus on February 20, 2021, 10:04:37 pm
@AndyA  well your post processing looks fabulous!
Title: Re: A dozen new and original IFS fractals
Post by: AndyA on February 21, 2021, 12:30:33 pm
Thanks bplus,

I believe the leaf itself turned out well, the background on the other hand... well, it was used as a backdrop rather hurriedly.

Just a reminder, if you use the IFS Viewer 3 app in JustBasic (until I can motivate myself to do the port to QB64), you can 1) plot an IFS fractal that you like then 2) press the 'Render Using an Image' button, choose an image from disk that you want to color the fractal with 3) save the .BMP of the fractal rendered using an image disk. Keep in mind the JustBasic is like 100 times slower than QB64, so plotting, and rendering with an image will take minutes, instead of seconds.

For placing on a custom background you'll need to mess with MS Paint and Paint.net using a couple of simple procedures to drop the fractal onto a nice background.

P.S. I forgot about the BlitzPlus version of IFS Viewer 3. It's waaaay faster than the JustBasic version. It can be found here https://socoder.net/?Showcase=54548 (https://socoder.net/?Showcase=54548)
Title: Re: A dozen new and original IFS fractals
Post by: OldMoses on February 21, 2021, 12:52:56 pm
These are amazing. I wish I had the ability to understand the stuff behind it.

Another thing that Tricera-fract reminds me of, being a bit of a Trekkie, it looks like a slight variation of the Klingon symbol.
Title: Re: A dozen new and original IFS fractals
Post by: AndyA on February 21, 2021, 01:17:15 pm
Hi OldMoses,

You know, I hadn't thought about it but, you're right I does look like a Klingon symbol. I'm surprised Johnno56, didn't mention that (just look at his avatar ).

[ edit]
Just a mild ribbing for Johnno56. I've talked to Johnno56 on and off over the last 5 years here and at other forums. I don't want him, or anyone else to think I meant anything mean or inappropriate. I meant it as a mild joke, but sometimes it doesn't seem like a joke in plain text.
[ /edit]
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