Mandelbulber V2.06 extended formulas EXAMPLES

[mclarekin]

Extended formulas were initially created as temporary formula tabs for experimentation with formula structures created in Mandelbulber V1 OpenCL. Benefits were being able to use faster analytic DE calculations, a huge increase in parameters available and greater flexibility while there were only four formula slots. Because they “exist”, it was decided to include them in the latest releases. The need for them will be superseded soon by an improved UI.

Since V2.05 the extended formula transform parameters names have been changed to begin with ”transform” , therefore  V2.05 extended formula parameter files will require editing to be compatible with V2.06. Likewise, in future, V2.06 extended formula parameter files may not be compatible with later versions.

The three new extended formulas tabs in V2.06 :-

Menger Extended.  Exploring hybridising mengers and/or mandelboxes. Plus various other transforms including the very cool BenesiMagTransformOne. All work well with analytic LinearDE

Mandelbulber6 Beta.  An analytic LogDE mandelbulb experimentation tab that includes

- the Mandelbulb-Multi transform that allows for 24 variations of trig Mandelbulb.

- Benesi Fast Pwr2 PineTree and MagTransformOne .

- experiments with varying constants based on iteration number.

Benesi_Transforms. Produced to experiment with Benesi PineTree and MagTransforms T1,T2,T3,T4 & T5b. Including mixing them with Menger and Mandelbox. This tab only covers a few of the many transforms recently created by M.Benesi. More Benesi Transforms will be coded soon.

All extended formula tabs have some experiments with color controls that will be superseded in future releases, but like the extended formulas, as they "exist" they have been released to play with.

[mclarekin]

This example is mainly formulas/transforms created by M.Benesi

We have four fractals poking thru the sand (yellow water effect from Primitives)

Multi-ray AO is used so if you want a faster render drop back to Screen Space AO

The Raymarching Step Multiplier needs to be dropped to below 0.5 for rendering,  (0.5 is good as often you will find that this parameter needs to be dropped to 0.1 when using some of the extended formulas.)

The Menger building is deformed by a BenesiMagTransformOne and more detail added by using two mengers with different parameters. Changing the start/stop iteration parameters  for the BenesiMagTransformOne (that is in all four formulas) , is where a lot of the fun is to be found.

Code:

# Mandelbulber settings file
# version 2.06
# only modified parameters
[main_parameters]
ambient_occlusion 2.5;
ambient_occlusion_enabled true;
ambient_occlusion_mode 1;
bailout 12;
boolean_operators true;
camera 0.4632794956672023 -4.300857222258994 0.39060399338144;
camera_distance_to_target 4;
camera_rotation 11.99999999999997 0 0;
camera_top 0 0 1;
coloring_palette_offset 24.52;
coloring_palette_size 255;
flight_last_to_render 0;
formula_1 55;
formula_2 58;
formula_3 58;
formula_4 58;
formula_position_2 -0.04 -3 -0.4;
formula_position_3 -0.84 -2.4 -0.65;
formula_position_4 0.5 -2.9 -0.2;
formula_rotation_2 0 145 0;
formula_rotation_3 0 145 0;
formula_rotation_4 0 145 0;
formula_scale_2 0.32;
formula_scale_3 0.6;
formula_scale_4 0.2;
fov 0.73;
fractal_rotation 0 125 0;
keyframe_last_to_render 0;
main_light_alpha -162.07;
primitive_water_1_color a300 9000 4b00;
primitive_water_1_enabled true;
primitive_water_1_iterations 3;
primitive_water_1_length 0.15;
primitive_water_1_position 0 0 -0.01;
primitive_water_1_rotation 0 0 47.12;
specular 0.4;
surface_color_palette 746c55 e0a15a a0501d e79a64 f39756 cf956f e9975d faa169 e39a4b aa7e3d f6b477 e5974c 615547 9a6636 cda13e be9b4a c2a24f c9aa50 c1a64f b89a51 b79c4f b89e54 b89c52 b3974e b39851 aaaa7f af9352 446382 1e568f bb6d25 ae6b1c dea33f 4e7b9c ffd236 6b868f 544a19 433600 524b45 206fa7 2383ab 13bbfa 301c1b efcf48 493905 2b1f09 efcf48 423807 2a2637 1cbcee 46baed 0fa8ec 33261e 914d00 fff35b d4a428 ffc962 5c3208 c48657 4cbad1 003849 58d4f8 119feb 3494be 231a13 c46900 4e2603 666670 2e899e 2dc8e7 2ba9d2 4eb7d5 1ba7dc 002d33 7e3807 ffe442 d4a726 633b00 724406 393431 1a5364 3ea6db 29adee 22d1ff 2ea9d5 22595e 843d00 f8bb2f 6a3800 bf963c 2c3637 40748a 91604f 5f210c ffd752 a56700 963200 fda619 117986 498087 0a8b9e 4a1b01 d75f09 e58038 7e5a4c 3a1d0d 653101 fed964 51646a 516472 73584f b34d1d bd4c14 59514f 6d6d61 604d47 564f45 2ea6f4 906255 403d38 373c42 47a8df 65585f fbc23d d28a1b d48c20 f9b52e ffeb3f c0722a c27229 c9701e d1932c c8942f c79325 c49529 dfa327 f9e351 d09e2f eda64e 786964 666874 80685e 5b9fb6 69625c 5d5854 976a40 c5ae6b f3df88 fde88f f1dd84 fbea92 ecd784 dac478 d1bb6f c9b56c d0ba6e e1ca7c ccb66a c2ae69 c8b16d c2a969 b49b63 b69d67 ae9763 b09965 cfb17d ac9c83 ae9d81 a9945b a7905a f1c155 e9b852 e5b354 d6a44d c59650 bb8d51 b78a51 bb9254 b38b4e b58d50 b68a4d b88a4e b2834d b2834d b7844f bc854c bb844c 7e6851 716046 5a564a 5d5542 735f44 785f49 5c584d 5f5742 796a4d 837a53 897b4c b5a34d c3ae55 d0b752 bd9d50 b7924b d0b043 d69464 ca8856 946d44 cf8757 e9ae76 bf804d a29851 a59852 deab76 e88d61 8d6e52 7e6c56 76654b 594f45 63594d 7c6752 7c6958 7a6850 6f6951 6b6356 6c6256 857d59 6a5c4f 7a6854 7c6651 786556 7c695a 68604b 6d5a4c 645a50 8a6753 886851 706b57 757156 7a7557 7c7354 827757 827555 897155 a2825b 92745c 8f6b55 645e50 7f6a4d 896952 866b56 8f7053 896e53 da9f63 766f55 726f4e 7e7151;
target -0.3683672676038351 -0.3882668193237716 0.3906039933814395;
[fractal_1]
transform_benesiMagTransformOne1_enabled true;
transform_benesiMagTransformOne1_stop_iterations 2;
transform_colorTrial1_enabled true;
transform_constantMultiplierOriginal1_enabled false;
transform_mandelbulbOriginal1_enabled false;
transform_mengerSponge2_constantZ 0.9;
transform_mengerSponge2_enabled true;
transform_mengerSponge2_factorConstantVect 1.3 2 1;
transform_mengerSponge2_start_iterations 4;
transform_mengerSpongeOriginal1_factorConstantVect 1.4 1 1;
transform_mengerSpongeOriginal1_start_iterations 3;
transform_mengerSpongeOriginal1_stop_iterations 6;
transform_variableScale2_scale 2 2 2;
[fractal_2]
transform_benesiMagTransformOneEnabled1_stop_iterations 3;
transform_coloringParameters1_enabled false;
transform_colorTrial1_axisBias_enabled true;
transform_colorTrial1_enabled true;
transform_colorTrial1_mainOTWeight 22;
transform_colorTrial1_minimumRWeight 0.001;
transform_colorTrial1_orbitTraps_enabled false;
[fractal_3]
transform_benesiMagTransformOneEnabled1_stop_iterations 2;
transform_coloringParameters1_enabled false;
transform_colorTrial1_axisBias_enabled true;
transform_colorTrial1_enabled true;
transform_colorTrial1_minimumRWeight 0.001;
transform_fabsAddConstant1_enabled true;
transform_fabsAddConstant1_stop_iterations 3;
transform_fabsAddConstant1B 1 1 1.1;
[fractal_4]
transform_benesiFastPwr2PineTreeEnabled1_constantMultiplier 1 0.4 0;
transform_benesiMagTransformOneEnabled1_stop_iterations 2;
transform_benesiMagTransformOnePlusMinus1_enabled true;
transform_benesiMagTransformOnePlusMinus1_start_iterations 2;
transform_benesiMagTransformOnePlusMinus1_stop_iterations 12;
transform_coloringParameters1_enabled false;
transform_colorTrial1_enabled true;
transform_colorTrial1_minimumRWeight 0.01;

[mclarekin]

This example is just a standard menger sponge with some Iteration Weight applied, ( located near the bottom of tab).

Disable Color Parameter groupBox ( second to bottom) and see what happens.

Enable  groupBox   z = fabs( z + const.A ) - fabs( z - const.B ) + ( z * const.C + const.D ); (16th groupBox from the top of the tab,)(an improved UI is needed) and see what happens.

What's good about all this is we are only using 3 transforms and we have  LinearDE, so this iexample is reasonable quick to render.  And OH NO!     I had the Raymarching Step Multiplier way down at 0.2. In fact I can bring it back up to 1.0, so faster still.

Code:

# Mandelbulber settings file
# version 2.06
# only modified parameters
[main_parameters]
ambient_occlusion_enabled true;
background_color_1 0000 6700 ac00;
background_color_2 0000 6700 ac00;
background_color_3 0000 6700 ac00;
camera -2.344386770935643 -5.523029120714641 0;
camera_distance_to_target 6;
camera_rotation -22.99999999999999 0 0;
camera_top 0 0 1;
coloring_palette_size 255;
DE_factor 0.2;
flight_last_to_render 0;
formula_1 55;
keyframe_last_to_render 0;
primitive_plane_1_enabled true;
primitive_plane_1_position 0 0 -1.5;
specular 0.4;
[fractal_1]
transform_colorTrial1_axisBias_enabled true;
transform_colorTrial1_enabled true;
transform_colorTrial1_orbitTraps_enabled false;
transform_fabsAddConstant1_enabled_x false;
transform_fabsAddConstant1_enabled_y false;
transform_fabsAddConstant1_enabled_z false;
transform_fabsFormulaABCD1_enabled_Az false;
transform_fabsFormulaABCD1_enabled_Bx false;
transform_fabsFormulaABCD1_enabled_By false;
transform_fabsFormulaABCD1_enabled_Bz false;
transform_fabsFormulaABCD1B 1 0 0;
transform_fabsFormulaABCD1C -0.2 0 1;
transform_fabsFormulaABCD2_enabled_Bx false;
transform_fabsFormulaABCD2_enabled_By false;
transform_fabsFormulaABCD2_enabled_Bz false;
transform_fabsFormulaABCD2C 0 0 0;
transform_iterationWeight1_constantA -1.2;
transform_iterationWeight1_enabled true;
transform_iterationWeight1_iterationA 1;
[fractal_2]
[fractal_3]
[fractal_4]

[M Benesi]

  I really like how you can position other fractals with Mandelbulber... That is cool. 

   Can you blend the formulas like we're talking about in the other thread (like a fractal will blend with another fractal where they intersect)?  Might be easiest to implement the spray gun in Mandelbulber. 

[mclarekin]

At the moment we have only 4 formula slots. But when we have more, i will be able to have a small forest of PineTrees rotating and morphing.

like a fractal will blend with another fractal where they intersect

I would think in  theory it looks possible,

[mclarekin]

Basic Benesi PineTree & magTransformOne

With both transforms try changing the start/stop parameters  and you will see the beginning of the amazing Benesi PineTree possibilities.(this set up is  fast for exploring using analytic LogDE )

Then add in  a few early iterations of some other transforms.

If the image quality/DE gets bad, try increasing the bailout on the Render_Engine tab before reducing the Ray Marching Step Multiplier  ( as it does not effect the render time as much),  and as a last resort you can tick Enable_hybrid_fractals on the Hybrid tab (this changes the DE calculation to DelatDE, which approx. doubles render time.)

# Mandelbulber settings file
# version 2.06
# only modified parameters
[main_parameters]
ambient_occlusion 3;
ambient_occlusion_enabled true;
ambient_occlusion_mode 1;
ambient_occlusion_quality 3;
aux_light_colour_1 f700 f700 f700;
aux_light_intensity_1 3.763638301968453e-05;
aux_light_position_1 0.4001095853924516 -1.301095327015237 0.9179749279703654;
aux_light_volumetric_enabled_1 true;
aux_light_volumetric_intensity_1 0.00457088;
background_color_1 0000 4e00 8200;
background_color_2 0000 4e00 8200;
background_color_3 0000 4e00 8200;
bailout 2;
brightness 1.2;
camera 0 -4 0.3;
camera_distance_to_target 4;
camera_rotation 0 0 0;
camera_top 0 0 1;
coloring_palette_offset 59.46;
coloring_palette_size 255;
DE_factor 0.4;
file_background /home/graeme/mandel textures/Inside a Mandelbulb Void.jpg;
file_lightmap /home/graeme/mandel textures/Hydrangeas.jpg;
flight_last_to_render 0;
fog_color_1 7500 7500 2d00;
formula_1 57;
fractal_rotation 0 -90 0;
image_width 600;
keyframe_last_to_render 0;
main_light_alpha -9.82;
main_light_beta 18;
specular 0.3;
SSAO_random_mode true;
surface_color_palette 746c55 e0a15a a0501d e79a64 f39756 cf956f e9975d faa169 e39a4b aa7e3d f6b477 e5974c 615547 9a6636 cda13e be9b4a c2a24f c9aa50 c1a64f b89a51 b79c4f b89e54 b89c52 b3974e b39851 b49952 af9352 446382 1e568f bb6d25 ae6b1c dea33f 4e7b9c ffd236 6b868f 544a19 433600 524b45 206fa7 2383ab 13bbfa 301c1b efcf48 493905 2b1f09 bfa314 423807 2a2637 1cbcee 46baed 0fa8ec 33261e 914d00 fff35b d4a428 ffc962 5c3208 c48657 4cbad1 003849 58d4f8 119feb 3494be 231a13 c46900 4e2603 666670 2e899e 2dc8e7 2ba9d2 4eb7d5 1ba7dc 002d33 7e3807 ffe442 d4a726 633b00 724406 393431 1a5364 3ea6db 29adee 22d1ff 2ea9d5 22595e 843d00 f8bb2f 6a3800 bf963c 2c3637 40748a 91604f 5f210c ffd752 a56700 963200 fda619 117986 498087 0a8b9e 4a1b01 d75f09 e58038 7e5a4c 3a1d0d 653101 fed964 51646a 516472 73584f b34d1d bd4c14 59514f 6d6d61 604d47 564f45 2ea6f4 906255 403d38 373c42 47a8df 65585f fbc23d d28a1b d48c20 f9b52e ffeb3f c0722a c27229 c9701e d1932c c8942f c79325 c49529 dfa327 f9e351 d09e2f eda64e 786964 666874 80685e 5b9fb6 69625c 5d5854 976a40 c5ae6b f3df88 fde88f f1dd84 fbea92 ecd784 dac478 d1bb6f c9b56c d0ba6e e1ca7c ccb66a c2ae69 c8b16d c2a969 b49b63 b69d67 ae9763 b09965 cfb17d ac9c83 ae9d81 a9945b a7905a f1c155 e9b852 e5b354 d6a44d c59650 bb8d51 b78a51 bb9254 b38b4e b58d50 b68a4d b88a4e b2834d b2834d b7844f bc854c bb844c 7e6851 716046 5a564a 5d5542 735f44 785f49 5c584d 5f5742 796a4d 837a53 897b4c b5a34d c3ae55 d0b752 bd9d50 b7924b d0b043 d69464 ca8856 946d44 cf8757 e9ae76 bf804d a29851 a59852 deab76 e88d61 8d6e52 7e6c56 76654b 594f45 63594d 7c6752 7c6958 7a6850 6f6951 6b6356 6c6256 857d59 6a5c4f 7a6854 7c6651 786556 7c695a 68604b 6d5a4c 645a50 8a6753 886851 706b57 757156 7a7557 7c7354 827757 827555 897155 a2825b 92745c 8f6b55 645e50 7f6a4d 896952 866b56 8f7053 896e53 da9f63 766f55 726f4e 7e7151;
target 0 0 0.3;
textured_background_map_type 1;
volumetric_fog_colour_1_distance 0.0001;
volumetric_fog_colour_2_distance 0.0002;
volumetric_fog_density 0.3;
volumetric_fog_distance_factor 0.0001;
[fractal_1]
transform_benesiFastPwr2PineTree1_enabled true;
transform_benesiMagTransformOne2_enabled true;
transform_benesiMagTransformOne2_start_iterations 3;
transform_constantMultiplierOriginal1_enabled false;
transform_fabsFormulaAB1_stop_iterations 2;
transform_fabsFormulaAB1A 0.6 0 0;
transform_fabsFormulaAB1B 0.6 0 0;
transform_mandelbulbOriginal1_enabled false;
[fractal_2]
[fractal_3]
[fractal_4]

[mclarekin]

This is  a single menger_sponge  with  a mixture of transforms applied

In this example there are a lot more parameters that have been adjusted from default.

To see what is happening try un-ticking the enabled  transforms one at a time then try adjusting parameters.

The menger_sponge parameters change size and shape of the menger_sponge.
The spherical offset simply keeps radially pushing the pixels away from the origin, and together with the spherical fold produce the curvature
The effect of scale does more than just size the image.
From feeble memory, the iteration weight works this way:-  When iteration number  =2,  the current z value is stored and multiplied by -0.3,  then added to the new current z at the end of each subsequent iteration loop.
BTW Remember I am not an expert and it would not be the first time if I am wrong or omit stuff in my posts, (you have been warned,. ).


Note. This is a fast fractal, hence I have not bothered to try lowering the stop iteration parameters to save render time.  They are all lazily set at 250. If I was animating I would test them.

# Mandelbulber settings file
# version 2.06
# only modified parameters
[main_parameters]
ambient_occlusion 1.3;
ambient_occlusion_enabled true;
ambient_occlusion_quality 10;
background_color_1 0000 6700 ac00;
background_color_2 0000 6700 ac00;
background_color_3 0000 6700 ac00;
camera -2.735117899424917 -6.443533974167083 0;
camera_rotation -22.99999999999999 0 0;
camera_top 0 0 1;
coloring_palette_size 255;
DE_factor 0.7;
flight_last_to_render 0;
formula_1 55;
image_width 600;
keyframe_last_to_render 0;
main_light_alpha 10.62;
specular 0.4;
[fractal_1]
transform_iterationWeight1_constantA -0.3;
transform_iterationWeight1_enabled true;
transform_iterationWeight1_iterationA 2;
transform_mengerSpongeOriginal1_constantZ 0.7;
transform_mengerSpongeOriginal1_factorConstantVect 1 1.3 1.2;
transform_scale2 -1.45;
transform_scale2_enabled true;
transform_sphericalFold2_enabled true;
transform_sphericalFold2_fixed_radius 1.35;
transform_sphericalFold2_min_radius 1;
transform_sphericalOffset1_offset_radius 0.8;
transform_sphericalOffset2_enabled true;
transform_sphericalOffset2_offset_radius 0.6;
[fractal_2]
[fractal_3]
[fractal_4]

[mclarekin]

This example is a simple Benesi PineTree - Quaternion hybrid.

Here we apply some quaternion influence to the PineTree, try changing the quaternion formula tab Iterations (at top of formula tab) from 1 up to 3 to the see the effect. Another way to see the effect is drop the quaternion formula tab's Weight down to 0 and back up to 1.0, you will see the quaternions  influence.

Code:

# Mandelbulber settings file
# version 2.06
# only modified parameters
[main_parameters]
ambient_occlusion_enabled true;
ambient_occlusion_quality 8;
background_color_1 0000 9500 ff00;
background_color_2 0000 9500 ff00;
background_color_3 0000 9500 ff00;
bailout 12;
camera 0 -4 0.1;
camera_distance_to_target 4;
camera_rotation 0 0 0;
camera_top 0 0 1;
DE_factor 0.1;
flight_last_to_render 0;
formula_1 58;
formula_2 54;
formula_iterations_2 3;
fractal_rotation 0 -90 0;
hybrid_fractal_enable true;
image_width 600;
keyframe_last_to_render 0;
main_light_alpha -22.44;
specular 0.4;
target 0 0 0.1;
[fractal_1]
transform_coloringParameters1_enabled false;
transform_colorTrial1_axisBias_enabled true;
transform_colorTrial1_colorConstant2 0;
transform_colorTrial1_colorConstant3 0;
transform_colorTrial1_enabled true;
transform_colorTrial1_orbitTraps_enabled false;
transform_constantMultiplierOriginal1_enabled false;
transform_mandelbulbMulti1_atan_or_atan2 1;
transform_mandelbulbOriginal1_enabled false;
transform_mengerSponge2_enabled true;
transform_mengerSpongeOriginal1_enabled false;
[fractal_2]
transform_constantMultiplierOriginal1 1 0 0;
[fractal_3]
[fractal_4]

[M Benesi]

lol   "fractal was prepared in newer version of Mandelbulber".  Time to download update.... I am such a slacker.


  Actually a bit has to do with learning a new environment, when I am still learning Fragmentarium and Mandelbulb3d.  Gotta get on it..

[mclarekin]

Benesi Transforms

The BenesiMagTransformOne (T1) is a powerful transform, not only does it make the Benesi Pine Tree mandebulb so amazing, but it  can be used to make all sorts of other hybrid fractals,  and does  real cool stuff when animated with rotations.

Below the images L to R,

  T1 inside  magForwards and magBack tranforms, (so a magTransform inside a magTransform)
   As above with one iteration of PineTree
  As above with Pinetree replaced with Benesi Cube to sphere transform

Code:

# Mandelbulber settings file
# version 2.06
# only modified parameters
[main_parameters]
ambient_occlusion_enabled true;
ambient_occlusion_quality 8;
background_color_1 0000 6200 a300;
background_color_2 0000 6200 a300;
background_color_3 0000 6200 a300;
bailout 12;
camera -0.000473324490501354 -3.990015811528487 0.00030322350172743;
camera_distance_to_target 4.961842288970947;
camera_rotation 2.714212216121742 1.737609031848171 0;
camera_top 0.001435891357942924 -0.03028833333160879 0.9995401718190228;
coloring_palette_size 30;
DE_factor 0.61;
flight_last_to_render 0;
formula_1 58;
fractal_rotation 0 0 90;
image_width 600;
keyframe_last_to_render 0;
specular 0;
surface_color_palette 5e869f 5d829d 5c819b 591600 320b06 744413 904907 d9140c 352611 212e12 19100b 150c07 e5b433 97b1d4 99b6d8 9dbbdd 9fc0e1 a1c2e1 a3c5e1 425209 a7c6da a4c3d7 a0bed6 98b9cc 92b3c6 88abbf 7ea2b8 749ab1 6b93ac 648ca5;
target -0.2353294718280259 0.963981046372421 0.1507579428898292;
[fractal_1]
transform_additionConstant2 -2 0 0;
transform_benesiFastPwr2PineTree1_stop_iterations 1;
transform_benesiFastPwr2PineTreeEnabled1_constantMultiplier 1 1 1;
transform_benesiFastPwr2PineTreeEnabled1_enabled false;
transform_benesiFastPwr2PineTreeEnabled1_start_iterations 1;
transform_benesiFastPwr2PineTreeEnabled1_stop_iterations 2;
transform_benesiMagBackTransformOne1_enabled true;
transform_benesiMagBackTransformOne1_stop_iterations 2;
transform_benesiMagForwardTransformOne1_enabled true;
transform_benesiMagTransformOneEnabled1_offset 2 0.5 0.9;
transform_benesiMagTransformOnePlusMinus1_start_iterations 3;
transform_benesiMagTransformOnePlusMinus1_stop_iterations 4;
transform_coloringParameters1_enabled false;
transform_colorTrial1_axisBias_enabled true;
transform_colorTrial1_colorConstant2 0;
transform_colorTrial1_colorConstant3 0;
transform_colorTrial1_enabled true;
transform_colorTrial1_mainOTWeight 22;
transform_constantMultiplierOriginal1_enabled false;
transform_cubeSphere1_enabled true;
transform_cubeSphere1_start_iterations 1;
transform_cubeSphere1_stop_iterations 2;
transform_mandelbulbOriginal1_enabled false;
transform_variableScale2_scale 2 2 2;
[fractal_2]
[fractal_3]
[fractal_4]
[fractal_5]
[fractal_6]
[fractal_7]
[fractal_8]
[fractal_9]

[mclarekin]

Collection of the T1 transform (on it's own) with the formula specific parameters tweaked.