# Linear Sim Tutorial – Whittaker Courtney

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Written By Whittaker Courtney

It started off when I was looking at the glynnsim3 code trying to alter the shape when I realized a similar thing could be recreated using 2 or 3 xforms with linears and post_smartcrops. This setup, although more complicated, allows much more customization than just using a glynnsim3 on its own.

Recreating the center could be done using a pre_spherical on the linear, which I know now to also be equivalent to the reciprocal of the complex number z. So in this tutorial I will be using pre_recip, as the additional variables can dramatically change the design in interesting ways, once it’s set up.

Just make sure to be using the latest version of JWildfire that should have it included. Pre variations work by being calculated before the other variations used on a transform and for some reason in JWildfire at least, the individual pre_variations sometimes have very different effects than just using the normal variation enabled as a “pre_variation”.

First to start off, create a new flame from scratch.

Add transform, change linear3d to objectmesh_primitive_wf and add primitives_wf as the 2nd variation on the same transform.
Set the amount on primitives_wf to 1 and change shape from 1 to 0.
Then change the amount on the objectmesh_primitive from 1 to 0.1 to set the width of the ring.

This should setup a ring shape to outline the pattern.

Add another new transform, then in addition to the linear3d, add pre_recip and set amount to 1.
Then add post_smartcrop, set the amount to 1, click the green triangle under the name to expand the list of variables, then set radius to 0.95, roundstr to 1, distortion to 0 and set cropmode to 2.

This transform will serve as the inner portion of the ring shape and will remove everything outside of the ring.

Finally add a new transform, change the amount on the linear3d to 1.2.
Then, in addition to the linear3d add post_smartcrop with amount set to 1, radius -1.05 (a negative radius to cut out a hole), roundstr to 1, distortion 0 and cropmode 2 to remove the outline.

This will create the outer shape with a hole cut out of the center for the inner shape to fit in.

Now the fun part. (You may want to zoom in a bit to better see the design)

Select transform 3, make sure Post TF is disabled and move the pre_transform triangle to the right by 0.5, then rotate counter-clockwise by 45 degrees.
You should see the entire pattern shift then form a spiral without having any rings overlap.
Next, select transform 2, click on the green triangle under the pre_recip variation name to expand the list of functions. You should be able to use your choice of any one of these individually and with reciprocal or sqrt also in combination to customize the inner design without any overlapping portions. ðŸ™‚

For further tweaks try experimenting with different settings, different pre_variations or other variations added in addition to the transform. Also you can try adding pre_recip and other pre_variations to the 3rd transform to modify the outer shape. If th pattern gets too dim to see, try increasing the weight of the transform. Finally, prepost_circlize can be added to all 3 xforms and the ring shape can be modified to form any number of sided shapes like a triangle, hexagon or octogon, etc.

Or you can use this template here.

```<flame smooth_gradient="0" version="JWildfire V4.10 (11.05.2019)" size="2560 1440" center="0.0 0.0" scale="570.0000127776791" 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" post_noise_filter="0" post_noise_filter_threshold="0.35" 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="4.0" 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_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="0.75" 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="300" fps="30" post_blur_radius="0" post_blur_fade="0.95" post_blur_falloff="2.0" zbuffer_scale="1.0" mixer_mode="OFF">
<xform weight="0.5" color_type="DIFFUSION" color="0.0" symmetry="0.0" mirror_pre_post_translations="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" obj_mesh_primitive_wf="0.1" obj_mesh_primitive_wf_fx_priority="0" obj_mesh_primitive_wf_primitive="0" obj_mesh_primitive_wf_scale_x="1.0" obj_mesh_primitive_wf_scale_y="1.0" obj_mesh_primitive_wf_scale_z="1.0" obj_mesh_primitive_wf_offset_x="0.0" obj_mesh_primitive_wf_offset_y="0.0" obj_mesh_primitive_wf_offset_z="0.0" obj_mesh_primitive_wf_subdiv_level="0" obj_mesh_primitive_wf_subdiv_smooth_passes="12" obj_mesh_primitive_wf_subdiv_smooth_lambda="0.42" obj_mesh_primitive_wf_subdiv_smooth_mu="-0.45" obj_mesh_primitive_wf_blend_colormap="1" obj_mesh_primitive_wf_displ_amount="0.1" obj_mesh_primitive_wf_blend_displ_map="1" obj_mesh_primitive_wf_receive_only_shadows="0" obj_mesh_primitive_wf_colormap_filename="" obj_mesh_primitive_wf_displ_map_filename="" primitives_wf="1.0" primitives_wf_fx_priority="0" primitives_wf_shape="0" primitives_wf_a="1.0" primitives_wf_b="1.0" primitives_wf_c="1.0" primitives_wf_filled="0" coefs="1.0 0.0 0.0 1.0 0.0 0.0" chaos="1.0 1.0 1.0"/>
<xform weight="0.5" color_type="DIFFUSION" color="0.0" symmetry="0.0" mirror_pre_post_translations="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" linear3D="1.0" linear3D_fx_priority="0" pre_recip="1.0" pre_recip_fx_priority="-1" pre_recip_reciprocalpow="1.0" pre_recip_dividepow="0.0" pre_recip_sqrtpow="1.0" pre_recip_asinhpow="0.0" pre_recip_acoshpow="0.0" pre_recip_atanhpow="1.0" pre_recip_asechpow="0.0" pre_recip_acosechpow="0.0" pre_recip_acothpow="0.0" pre_recip_logpow="0.0" pre_recip_exppow="0.0" pre_recip_zx_mult="1.0" pre_recip_zy_mult="1.0" pre_recip_zx_add="0.0" pre_recip_zy_add="0.0" post_smartcrop="1.0" post_smartcrop_fx_priority="1" post_smartcrop_power="4.0" post_smartcrop_radius="0.95" post_smartcrop_roundstr="1.0" post_smartcrop_roundwidth="1.0" post_smartcrop_distortion="0.0" post_smartcrop_edge="0.0" post_smartcrop_scatter="0.0" post_smartcrop_offset="0.0" post_smartcrop_cropmode="2" post_smartcrop_static="2" coefs="1.0 0.0 0.0 1.0 0.0 0.0" chaos="1.0 1.0 1.0"/>
<xform weight="0.5" color_type="DIFFUSION" color="0.0" symmetry="0.0" mirror_pre_post_translations="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" linear3D="1.2" linear3D_fx_priority="0" post_smartcrop="1.0" post_smartcrop_fx_priority="1" post_smartcrop_power="4.0" post_smartcrop_radius="-1.05" post_smartcrop_roundstr="1.0" post_smartcrop_roundwidth="1.0" post_smartcrop_distortion="0.0" post_smartcrop_edge="0.0" post_smartcrop_scatter="0.0" post_smartcrop_offset="0.0" post_smartcrop_cropmode="2" post_smartcrop_static="2" coefs="0.7071067811865476 -0.7071067811865475 0.7071067811865475 0.7071067811865476 0.5 0.0" chaos="1.0 1.0 1.0"/>
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