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 Post subject: Perfect Blurring
PostPosted:Wed Apr 28, 2021 11:38 pm 
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Joined:Mon Jun 03, 2013 7:44 am
Posts:220
Many times when we create fractal flames, we utilize random (pContext.random()) to create blurs necessary for the "solid" parts of our fractal. Unfortunately, what happens is that we get a grainy effect (in certain areas) that can only be filled in by continuous rendering over a long period of time. The clarity of our fractal is at the mercy of the random number generator. This is wasteful of computer processing time and doesn't produce the beautiful images we want. We could compensate by using post processing visual effects to remove the graininess, but that still requires a wasted period of rendering time.

Consider the following fractal that uses a standard blur:
Code:
<flame smooth_gradient="0" version="JWildfire V6.50 (11.04.2021)" size="1280 1024" center="0.0 0.0" scale="82.6666891624684" rotate="0.0" filter="0.75" filter_type="GLOBAL_SHARPENING" filter_kernel="MITCHELL_SMOOTH" filter_indicator="0" filter_sharpness="4.0" filter_low_density="0.025" oversample="1" ai_post_denoiser="NONE" post_optix_denoiser_blend="0.11111" quality="100.0" background_type="GRADIENT_2X2_C" background_ul="0.0 0.0 0.0" background_ur="0.0 0.0 0.0" background_ll="0.0 0.0 0.0" background_lr="0.0 0.0 0.0" background_cc="0.0 0.0 0.0" bg_transparency="0" fg_opacity="1.0" brightness="1000.0" saturation="1.0" gamma="4.0" gamma_threshold="0.01" vibrancy="1.0" contrast="1.0" white_level="220.0" temporal_samples="1.0" cam_zoom="1.0" cam_pitch="0.0" cam_yaw="0.0" cam_roll="0.0" cam_persp="0.0" cam_xfocus="0.0" cam_yfocus="0.0" cam_zfocus="0.0" cam_pos_x="0.0" cam_pos_y="0.0" cam_pos_z="0.0" cam_zpos="0.0" cam_dof="0.0" cam_dof_area="0.5" cam_dof_exponent="2.0" low_density_brightness="0.24" balancing_red="1.0" balancing_green="1.0" balancing_blue="1.0" cam_dof_shape="BUBBLE" cam_dof_scale="1.0" cam_dof_rotate="0.0" cam_dof_fade="1.0" antialias_amount="0.25" antialias_radius="0.5" post_symmetry_type="NONE" post_symmetry_order="3" post_symmetry_centre_x="0.0" post_symmetry_centre_y="0.0" post_symmetry_distance="1.25" post_symmetry_rotation="6.0" frame="1" frame_count="100" fps="25" post_blur_radius="0" post_blur_fade="0.95" post_blur_falloff="2.0" zbuffer_scale="1.0" zbuffer_bias="0.0" zbuffer_filename="PRE_ZBUF" brightnessCurve_enabled="false" brightnessCurve_view_xmin="0" brightnessCurve_view_xmax="2" brightnessCurve_view_ymin="1000.0" brightnessCurve_view_ymax="1000.0" brightnessCurve_interpolation="SPLINE" brightnessCurve_selected_idx="0" brightnessCurve_locked="false" brightnessCurve_point_count="1" brightnessCurve_x0="1" brightnessCurve_y0="1000.0" mixer_mode="OFF" grad_edit_hue_curve_enabled="false" grad_edit_hue_curve_view_xmin="-5" grad_edit_hue_curve_view_xmax="260" grad_edit_hue_curve_view_ymin="-5.0" grad_edit_hue_curve_view_ymax="260.0" grad_edit_hue_curve_interpolation="SPLINE" grad_edit_hue_curve_selected_idx="0" grad_edit_hue_curve_locked="false" grad_edit_hue_curve_point_count="11" grad_edit_hue_curve_x0="0" grad_edit_hue_curve_y0="188.69999999999996" grad_edit_hue_curve_x1="9" grad_edit_hue_curve_y1="23.611111111111118" grad_edit_hue_curve_x2="34" grad_edit_hue_curve_y2="103.27102803738319" grad_edit_hue_curve_x3="54" grad_edit_hue_curve_y3="97.33870967741937" grad_edit_hue_curve_x4="80" grad_edit_hue_curve_y4="34.06028368794326" grad_edit_hue_curve_x5="109" grad_edit_hue_curve_y5="19.499999999999996" grad_edit_hue_curve_x6="126" grad_edit_hue_curve_y6="167.8284671532847" grad_edit_hue_curve_x7="142" grad_edit_hue_curve_y7="172.72435897435895" grad_edit_hue_curve_x8="174" grad_edit_hue_curve_y8="12.966101694915242" grad_edit_hue_curve_x9="183" grad_edit_hue_curve_y9="23.405797101449277" grad_edit_hue_curve_x10="255" grad_edit_hue_curve_y10="7.291666666666664" grad_edit_saturation_curve_enabled="false" grad_edit_saturation_curve_view_xmin="-5" grad_edit_saturation_curve_view_xmax="260" grad_edit_saturation_curve_view_ymin="-5.0" grad_edit_saturation_curve_view_ymax="260.0" grad_edit_saturation_curve_interpolation="SPLINE" grad_edit_saturation_curve_selected_idx="0" grad_edit_saturation_curve_locked="false" grad_edit_saturation_curve_point_count="11" grad_edit_saturation_curve_x0="0" grad_edit_saturation_curve_y0="236.11111111111117" grad_edit_saturation_curve_x1="29" grad_edit_saturation_curve_y1="232.07865168539325" grad_edit_saturation_curve_x2="49" grad_edit_saturation_curve_y2="119.14847161572051" grad_edit_saturation_curve_x3="72" grad_edit_saturation_curve_y3="104.47136563876653" grad_edit_saturation_curve_x4="96" grad_edit_saturation_curve_y4="255.0" grad_edit_saturation_curve_x5="120" grad_edit_saturation_curve_y5="238.18681318681317" grad_edit_saturation_curve_x6="141" grad_edit_saturation_curve_y6="244.30069930069936" grad_edit_saturation_curve_x7="154" grad_edit_saturation_curve_y7="255.0" grad_edit_saturation_curve_x8="175" grad_edit_saturation_curve_y8="231.46153846153854" grad_edit_saturation_curve_x9="195" grad_edit_saturation_curve_y9="255.0" grad_edit_saturation_curve_x10="255" grad_edit_saturation_curve_y10="240.83333333333334" grad_edit_luminosity_curve_enabled="false" grad_edit_luminosity_curve_view_xmin="-5" grad_edit_luminosity_curve_view_xmax="260" grad_edit_luminosity_curve_view_ymin="-5.0" grad_edit_luminosity_curve_view_ymax="260.0" grad_edit_luminosity_curve_interpolation="SPLINE" grad_edit_luminosity_curve_selected_idx="0" grad_edit_luminosity_curve_locked="false" grad_edit_luminosity_curve_point_count="11" grad_edit_luminosity_curve_x0="0" grad_edit_luminosity_curve_y0="214.5" grad_edit_luminosity_curve_x1="8" grad_edit_luminosity_curve_y1="210.5" grad_edit_luminosity_curve_x2="33" grad_edit_luminosity_curve_y2="140.5" grad_edit_luminosity_curve_x3="44" grad_edit_luminosity_curve_y3="113.5" grad_edit_luminosity_curve_x4="53" grad_edit_luminosity_curve_y4="184.5" grad_edit_luminosity_curve_x5="62" grad_edit_luminosity_curve_y5="45.5" grad_edit_luminosity_curve_x6="78" grad_edit_luminosity_curve_y6="71.5" grad_edit_luminosity_curve_x7="104" grad_edit_luminosity_curve_y7="39.0" grad_edit_luminosity_curve_x8="113" grad_edit_luminosity_curve_y8="222.5" grad_edit_luminosity_curve_x9="129" grad_edit_luminosity_curve_y9="69.0" grad_edit_luminosity_curve_x10="255" grad_edit_luminosity_curve_y10="147.0" palette_modShiftCurve_enabled="false" palette_modShiftCurve_view_xmin="0" palette_modShiftCurve_view_xmax="2" palette_modShiftCurve_view_ymin="97.0" palette_modShiftCurve_view_ymax="97.0" palette_modShiftCurve_interpolation="SPLINE" palette_modShiftCurve_selected_idx="0" palette_modShiftCurve_locked="false" palette_modShiftCurve_point_count="1" palette_modShiftCurve_x0="1" palette_modShiftCurve_y0="97.0">
  <xform weight="0.5" color_type="DIFFUSION" color="0.0" symmetry="0.0" material="0.0" material_speed="0.0" mod_gamma="0.0" mod_gamma_speed="0.0" mod_contrast="0.0" mod_contrast_speed="0.0" mod_saturation="0.0" mod_saturation_speed="0.0" mod_hue="0.0" mod_hue_speed="0.0" opacity="0.0" blur="1.0" blur_fx_priority="0" blur_amountCurve_enabled="false" blur_amountCurve_view_xmin="0" blur_amountCurve_view_xmax="2" blur_amountCurve_view_ymin="1.0" blur_amountCurve_view_ymax="1.0" blur_amountCurve_interpolation="SPLINE" blur_amountCurve_selected_idx="0" blur_amountCurve_locked="false" blur_amountCurve_point_count="1" blur_amountCurve_x0="1" blur_amountCurve_y0="1.0" coefs="1.0 0.0 0.0 1.0 0.0 0.0" chaos="1.0 1.0 0.0"/>
  <xform weight="0.5" color_type="DIFFUSION" color="0.0" symmetry="0.0" material="0.0" material_speed="0.0" mod_gamma="0.0" mod_gamma_speed="0.0" mod_contrast="0.0" mod_contrast_speed="0.0" mod_saturation="0.0" mod_saturation_speed="0.0" mod_hue="0.0" mod_hue_speed="0.0" opacity="0.0" cross="1.0" cross_fx_priority="0" coefs="1.0 0.0 0.0 1.0 0.0 0.0" chaos="0.0 0.0 1.0"/>
  <xform weight="0.5" color_type="NONE" color="0.0" symmetry="1.0" material="0.0" material_speed="0.0" mod_gamma="0.0" mod_gamma_speed="0.0" mod_contrast="0.0" mod_contrast_speed="0.0" mod_saturation="0.0" mod_saturation_speed="0.0" mod_hue="0.0" mod_hue_speed="0.0" julian="5.0" julian_fx_priority="0" julian_power="-5" julian_dist="1.0" julian_amountCurve_enabled="false" julian_amountCurve_view_xmin="0" julian_amountCurve_view_xmax="2" julian_amountCurve_view_ymin="5.0" julian_amountCurve_view_ymax="5.0" julian_amountCurve_interpolation="SPLINE" julian_amountCurve_selected_idx="0" julian_amountCurve_locked="false" julian_amountCurve_point_count="1" julian_amountCurve_x0="1" julian_amountCurve_y0="5.0" coefs="1.0 0.0 0.0 1.0 0.0 0.0" chaos="1.0 0.0 0.0"/>
  <palette count="256" format="RGB">
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</flame>
Having thought about it, I decided a more effective approach might be to create a better blur variation: one that positions points exactly in an iterative fashion around a circle, thereby nearly guaranteeing that every point within that circle got represented. Obviously, pixels don't correlate one-to-one with fractal pixels and there will be some scaling issues, so it's necessary to create more points than pixels.
With this in mind, I tried to approaches:
The first approach was to create a series of lines (made of N number of points) and iterating them around in a circle (so there would be M number of lines in the circle). The lines were made by incrementing little by little outward until the line was completed, then the angle would be incremented and a new line begin. As N and M increased, so did point density.
The second approach was to create rings (made of N number of points) and iterating them inward until reaching the center. Again, each ring was created by creating a point and then incrementing a fraction of a degree to create the next point until the full circle was created.

I then replaced the blur of the aforementioned fractal with these two custom variation blurs. The first blur turned out to be strong on the outside but you could see lonely arcs near the center. The second blur was strong on the inside but lonely arcs existed on the outside. To their credit, on their own, they produced strong fractal shapes without the graininess the other blurs gave. Combined, they produced some graininess, but their strength on both the inside and outside was awesome. Check it out:
Code:
<flame smooth_gradient="0" version="JWildfire V6.50 (11.04.2021)" size="1280 1024" center="0.0 0.0" scale="82.66670041037156" rotate="0.0" filter="0.75" filter_type="GLOBAL_SHARPENING" filter_kernel="MITCHELL_SMOOTH" filter_indicator="0" filter_sharpness="4.0" filter_low_density="0.025" oversample="1" ai_post_denoiser="NONE" post_optix_denoiser_blend="0.11111" quality="100.0" background_type="GRADIENT_2X2_C" background_ul="0.0 0.0 0.0" background_ur="0.0 0.0 0.0" background_ll="0.0 0.0 0.0" background_lr="0.0 0.0 0.0" background_cc="0.0 0.0 0.0" bg_transparency="0" fg_opacity="1.0" brightness="1000.0" saturation="1.0" gamma="4.0" gamma_threshold="0.01" vibrancy="1.0" contrast="1.0" white_level="220.0" temporal_samples="1.0" cam_zoom="1.0" cam_pitch="0.0" cam_yaw="0.0" cam_roll="0.0" cam_persp="0.0" cam_xfocus="0.0" cam_yfocus="0.0" cam_zfocus="0.0" cam_pos_x="0.0" cam_pos_y="0.0" cam_pos_z="0.0" cam_zpos="0.0" cam_dof="0.0" cam_dof_area="0.5" cam_dof_exponent="2.0" low_density_brightness="0.24" balancing_red="1.0" balancing_green="1.0" balancing_blue="1.0" cam_dof_shape="BUBBLE" cam_dof_scale="1.0" cam_dof_rotate="0.0" cam_dof_fade="1.0" antialias_amount="0.25" antialias_radius="0.5" post_symmetry_type="NONE" post_symmetry_order="3" post_symmetry_centre_x="0.0" post_symmetry_centre_y="0.0" post_symmetry_distance="1.25" post_symmetry_rotation="6.0" frame="1" frame_count="100" fps="25" post_blur_radius="0" post_blur_fade="0.95" post_blur_falloff="2.0" zbuffer_scale="1.0" zbuffer_bias="0.0" zbuffer_filename="PRE_ZBUF" brightnessCurve_enabled="false" brightnessCurve_view_xmin="0" brightnessCurve_view_xmax="2" brightnessCurve_view_ymin="1000.0" brightnessCurve_view_ymax="1000.0" brightnessCurve_interpolation="SPLINE" brightnessCurve_selected_idx="0" brightnessCurve_locked="false" brightnessCurve_point_count="1" brightnessCurve_x0="1" brightnessCurve_y0="1000.0" mixer_mode="OFF" grad_edit_hue_curve_enabled="false" grad_edit_hue_curve_view_xmin="-5" grad_edit_hue_curve_view_xmax="260" grad_edit_hue_curve_view_ymin="-5.0" grad_edit_hue_curve_view_ymax="260.0" grad_edit_hue_curve_interpolation="SPLINE" grad_edit_hue_curve_selected_idx="0" grad_edit_hue_curve_locked="false" grad_edit_hue_curve_point_count="11" grad_edit_hue_curve_x0="0" grad_edit_hue_curve_y0="188.69999999999996" grad_edit_hue_curve_x1="9" grad_edit_hue_curve_y1="23.611111111111118" grad_edit_hue_curve_x2="34" grad_edit_hue_curve_y2="103.27102803738319" grad_edit_hue_curve_x3="54" grad_edit_hue_curve_y3="97.33870967741937" grad_edit_hue_curve_x4="80" grad_edit_hue_curve_y4="34.06028368794326" grad_edit_hue_curve_x5="109" grad_edit_hue_curve_y5="19.499999999999996" grad_edit_hue_curve_x6="126" grad_edit_hue_curve_y6="167.8284671532847" grad_edit_hue_curve_x7="142" grad_edit_hue_curve_y7="172.72435897435895" grad_edit_hue_curve_x8="174" grad_edit_hue_curve_y8="12.966101694915242" grad_edit_hue_curve_x9="183" grad_edit_hue_curve_y9="23.405797101449277" grad_edit_hue_curve_x10="255" grad_edit_hue_curve_y10="7.291666666666664" grad_edit_saturation_curve_enabled="false" grad_edit_saturation_curve_view_xmin="-5" grad_edit_saturation_curve_view_xmax="260" grad_edit_saturation_curve_view_ymin="-5.0" grad_edit_saturation_curve_view_ymax="260.0" grad_edit_saturation_curve_interpolation="SPLINE" grad_edit_saturation_curve_selected_idx="0" grad_edit_saturation_curve_locked="false" grad_edit_saturation_curve_point_count="11" grad_edit_saturation_curve_x0="0" grad_edit_saturation_curve_y0="236.11111111111117" grad_edit_saturation_curve_x1="29" grad_edit_saturation_curve_y1="232.07865168539325" grad_edit_saturation_curve_x2="49" grad_edit_saturation_curve_y2="119.14847161572051" grad_edit_saturation_curve_x3="72" grad_edit_saturation_curve_y3="104.47136563876653" grad_edit_saturation_curve_x4="96" grad_edit_saturation_curve_y4="255.0" grad_edit_saturation_curve_x5="120" grad_edit_saturation_curve_y5="238.18681318681317" grad_edit_saturation_curve_x6="141" grad_edit_saturation_curve_y6="244.30069930069936" grad_edit_saturation_curve_x7="154" grad_edit_saturation_curve_y7="255.0" grad_edit_saturation_curve_x8="175" grad_edit_saturation_curve_y8="231.46153846153854" grad_edit_saturation_curve_x9="195" grad_edit_saturation_curve_y9="255.0" grad_edit_saturation_curve_x10="255" grad_edit_saturation_curve_y10="240.83333333333334" grad_edit_luminosity_curve_enabled="false" grad_edit_luminosity_curve_view_xmin="-5" grad_edit_luminosity_curve_view_xmax="260" grad_edit_luminosity_curve_view_ymin="-5.0" grad_edit_luminosity_curve_view_ymax="260.0" grad_edit_luminosity_curve_interpolation="SPLINE" grad_edit_luminosity_curve_selected_idx="0" grad_edit_luminosity_curve_locked="false" grad_edit_luminosity_curve_point_count="11" grad_edit_luminosity_curve_x0="0" grad_edit_luminosity_curve_y0="214.5" grad_edit_luminosity_curve_x1="8" grad_edit_luminosity_curve_y1="210.5" grad_edit_luminosity_curve_x2="33" grad_edit_luminosity_curve_y2="140.5" grad_edit_luminosity_curve_x3="44" grad_edit_luminosity_curve_y3="113.5" grad_edit_luminosity_curve_x4="53" grad_edit_luminosity_curve_y4="184.5" grad_edit_luminosity_curve_x5="62" grad_edit_luminosity_curve_y5="45.5" grad_edit_luminosity_curve_x6="78" grad_edit_luminosity_curve_y6="71.5" grad_edit_luminosity_curve_x7="104" grad_edit_luminosity_curve_y7="39.0" grad_edit_luminosity_curve_x8="113" grad_edit_luminosity_curve_y8="222.5" grad_edit_luminosity_curve_x9="129" grad_edit_luminosity_curve_y9="69.0" grad_edit_luminosity_curve_x10="255" grad_edit_luminosity_curve_y10="147.0" palette_modShiftCurve_enabled="false" palette_modShiftCurve_view_xmin="0" palette_modShiftCurve_view_xmax="2" palette_modShiftCurve_view_ymin="97.0" palette_modShiftCurve_view_ymax="97.0" palette_modShiftCurve_interpolation="SPLINE" palette_modShiftCurve_selected_idx="0" palette_modShiftCurve_locked="false" palette_modShiftCurve_point_count="1" palette_modShiftCurve_x0="1" palette_modShiftCurve_y0="97.0">
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</flame>
On my PC, it only took a minute and four seconds to render an almost completely solid shape. The arches in the center would take a very long time to eliminate, but they don't hurt the image.
Overall, I'm very pleased with the results.

_________________
Fractal artwork: http://ablipintime.deviantart.com


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 Post subject: Re: Perfect Blurring
PostPosted:Thu Apr 29, 2021 3:55 pm 
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Joined:Sun May 31, 2015 2:39 pm
Posts:695
interesting idea but then it leave little lines behind.
If you use one of the built in de-noisers you will not get the "specks"


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 Post subject: Re: Perfect Blurring
PostPosted:Fri Apr 30, 2021 11:48 pm 
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Site Admin
User avatar

Joined:Wed May 15, 2013 10:28 pm
Posts:1556
Interesting!

This looks like some kind of rasterization. It is also used in the svg-variation, for example.

To get a solid circular shape you could also use sineblur with a power of 5, for example.

Cheers!
Code:
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grad_edit_saturation_curve_y2="119.14847161572051" grad_edit_saturation_curve_x3="72" grad_edit_saturation_curve_y3="104.47136563876653" grad_edit_saturation_curve_x4="96" grad_edit_saturation_curve_y4="255.0" grad_edit_saturation_curve_x5="120" grad_edit_saturation_curve_y5="238.18681318681317" grad_edit_saturation_curve_x6="141" grad_edit_saturation_curve_y6="244.30069930069936" grad_edit_saturation_curve_x7="154" grad_edit_saturation_curve_y7="255.0" grad_edit_saturation_curve_x8="175" grad_edit_saturation_curve_y8="231.46153846153854" grad_edit_saturation_curve_x9="195" grad_edit_saturation_curve_y9="255.0" grad_edit_saturation_curve_x10="255" grad_edit_saturation_curve_y10="240.83333333333334" grad_edit_luminosity_curve_enabled="false" grad_edit_luminosity_curve_view_xmin="-5" grad_edit_luminosity_curve_view_xmax="260" grad_edit_luminosity_curve_view_ymin="-5.0" grad_edit_luminosity_curve_view_ymax="260.0" grad_edit_luminosity_curve_interpolation="SPLINE" grad_edit_luminosity_curve_selected_idx="0" grad_edit_luminosity_curve_locked="false" grad_edit_luminosity_curve_point_count="11" grad_edit_luminosity_curve_x0="0" grad_edit_luminosity_curve_y0="214.5" grad_edit_luminosity_curve_x1="8" grad_edit_luminosity_curve_y1="210.5" grad_edit_luminosity_curve_x2="33" grad_edit_luminosity_curve_y2="140.5" grad_edit_luminosity_curve_x3="44" grad_edit_luminosity_curve_y3="113.5" grad_edit_luminosity_curve_x4="53" grad_edit_luminosity_curve_y4="184.5" grad_edit_luminosity_curve_x5="62" grad_edit_luminosity_curve_y5="45.5" grad_edit_luminosity_curve_x6="78" grad_edit_luminosity_curve_y6="71.5" grad_edit_luminosity_curve_x7="104" grad_edit_luminosity_curve_y7="39.0" grad_edit_luminosity_curve_x8="113" grad_edit_luminosity_curve_y8="222.5" grad_edit_luminosity_curve_x9="129" grad_edit_luminosity_curve_y9="69.0" grad_edit_luminosity_curve_x10="255" grad_edit_luminosity_curve_y10="147.0" palette_modShiftCurve_enabled="false" 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