# Objective of this tutorial

In this tutorial we want to show how to combine different formulas/variations and how to change parameters of formulas. Please note, that there is no difference between formulas and variations, but I prefer the term "formula" because it is more precise.

# Create a new empty fractal with a blurring formula

To get started, create a new empty fractal by hitting the New from scratch-button. Have a look at the Gradient-tab, when you do not like the randomly created gradient, just hit the New from scratch again. And again if you are not satisfied yet...

Add a new transform by pressing the Add-button on the Transformations-tab. Change the variation 1 from "linear3D" to "circleblur", you should see a filled circle in the viewport. But, when you drag the controls around, you will see, that the shape does not change. But, why? To understand this, we must look at formulas more close. There are different types.

## Types of formulas/variations

There are two major categories of formulas:

1. transforming formulas: formulas which change an existing part of the fractal, where the detail of the original is not changed.

For example, a wave-transformation applied to an existing fractal will just make it "wavy", but not increase or decrease the detail very much. I.e., a transforming formula contributes to the overall transform.

1. blurring formulas: formulas who completely ignore the existing fractal and create new shape.

For example, "circleblur" will always create a filled circle, and not transform the existing structure, it will replace it. I.e., used in this simple scenario, a blurring formula overwrites the transforms, so that it is not a conventional transform anymore.

That also means that it isn't possible to create fractals by using only blurring formulas, because you need transforms to create the typical fractal (i. e. self-similar) structure. You need some transform, which transforms some transformed stuff, which was transformed by ..., and so on. But blurring formulas, when used at the right place, are really great for constructing flames from scratch.

# Add a second transform with a transforming formula

Now add a second transform and change the variation 2 from "linear3D" to "julian", you should not see much difference in the viewport yet.

## Formulas with parameter

The formula you chose is a formula with additional parameters. For such formulas you use the listbox below the listbox which show the name the of the formula to select a a parameter, and the edit-field right of it to change the value of this parameter.
Please note, that not all parameters are just numbers, some formulas even have complex structures like images as parameters, in this case you may find more controls right of this field. Please change the value of the parameter power of the "julian"-formula to 2. Then use your mouse to modify the seconds transform (the one with "julian"-formula on it). Enlarge the control, rotate it and move it in the viewport until you get something like this: The fractal is still monochrome, to change this enter the Color-tab on the Transformations-tab, and modify the Color-slider ## Changing formula params

Now let's play again with the parameters of the "julian"-variation to show how small parameter-changes can cause huge differences in the final result. Change "power" to 3, and "dist" to 1.76.

You have three choices for how to do this:

1. Enter the value directly (which is only a choice if you know the value, i. e. not for playing around)
2. Enter the field with the mouse, click and hold the left mouse-button and move the mouse to decrease/increase the value (best for playing around)
3. Use the small arrow-buttons to slightly decrease/increase the value (best for fine-adjustments)

Your flame should look like this (if not you may compare your result with the flame-params which are supplied in the appendix): ### Fine adjustment of parameters

Sometimes the parameter-changes done by using the mouse or the arrow-buttons are too large for, even if done carefully. For this purpose you can activate the Fine-button at the top of the editor-area. All changes, you do now, are scaled down by a factor of approximately 10. # Conclusion

We have learned how to use different formulas in one fractal, how to change formulas and that there two types of formula (transforming and blurring formula). And we saw how to change parameters of formulas and that also small changes to parameters of formulas may have a large impact on the final image.

# Appendix

## Params of the final sample flame

```<flame smooth_gradient="0" version="JWildfire 2.34 (22.02.2015)" size="643 362" center="0.0 0.0" scale="35.17734553722945" rotate="0.0" filter="0.0" filter_kernel="GAUSSIAN" quality="10.0" background="0.0 0.0 0.0" bg_transparency="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" cam_dof_shape="BUBBLE" cam_dof_scale="1.0" cam_dof_rotate="0.0" cam_dof_fade="1.0" shading_shading="FLAT" antialias_amount="0.75" antialias_radius="0.36" 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" mixer_mode="OFF" >
<xform weight="0.5" color="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" symmetry="0.0" circleblur="1.0" coefs="1.0 0.0 0.0 1.0 0.0 0.0" chaos="1.0 1.0" />
<xform weight="0.5" color="0.39" 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" symmetry="0.0" julian="1.0" julian_power="3" julian_dist="1.76" coefs="1.8747239284667137 1.1869473754012025 -1.1869473754012025 1.8747239284667137 3.3237513474667604 -0.8341460910630871" chaos="1.0 1.0" />
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