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]