As you can see the expression maps out rather easily to a node tree. The iterate node looks a little funny as we have to assume it has some mechanism for determinig what it should repeat. And the let node maps oddly because it establishes a lexical scope in lisp code, but in a node structure it would just provide a few attributes for other nodes to manipulate. On the balance, it's a rather good approximation.

From here on out, we can visualize fBm as a single node with five inputs and single numeric output. That's the beauty of syntactic expressions, since they are atomic, it's easy to replace a function's expansion with its name to abstract away complexity. In Houdini, this would be the equivalent of collapsing a group of nodes into a subnet.

Let's use the new fBm node to construct a flame shader. Basically a flame shader is made up of three components, a color ramp from yellow to red, an opacity mask to make it wispy, and a displacement to deform the object. Each of these involves fBm to generate layers of noise. So we can visualize the bottom of the tree as our complete shader, and the three nodes immediately abouve it must be Ci (the color information), Oi (opacity), and displace. As a syntactic expression it might look like "(shader Ci Oi displace)".

The next step will be to expand each of those in to their components. Starting with Ci, we know we need to be able to use two colors, fBm, and the value of t, the vertical axis of texture space. So we can expand Ci to look like "(Ci color1 color2 fBm t)". Obviously fBm will need some parameters so the next level of expansion migh look like "(Ci color1 color2 (fBm P oct lac gain) t)".

Moving on to Oi, it can depends on t and fBm. Oi can use the same parameters for fBm, which will generate the same output. Oi becomes "(Oi t (fBm P oct lac gain))".

Displace depends on a cos moving along the t axis, and noise. It can be written as "(displace (cos t) (fBm P oct2 lac2 gain2))". Note that displace feeds different parameters to fBm, that will result in different output. It would appear in a node tree as a seperate instance of a fBm node, whereas Ci and Oi share an FBm node.

At this point the flame share looks like this

(shader
 (Ci color1 color2 (fBm P oct lac gain) t)
 (Oi t (fBm P oct lac gain))
 (displace (cos t) (fBm P oct2 lac2 gain2)))

The user of this shader will probably want to be able to play with the settings so we should probably add another element called user parameters to the syntatcic expression. At this point we can also draw it as a complete node tree

(shader (user-parameters)
 (Ci color1 color2 (fBm P oct lac gain) t)
 (Oi t (fBm P oct lac gain))
 (displace (+ (cos t) (fBm P oct2 lac2 gain2))))

At this point the only things left to do are actually define, how the functions Ci, Oi, and displace work and convert the shader definition to renderman shading language so we can use it.

(defun displace (amt)
  (calculatenormal (+ P (* (normalize N) amt))))

(defun Ci (color1 color2 noise_val height)
  (mix color1 color2 (smoothstep 0 1 (- noise_val height))))

(defun Oi (height noise_val)
  (let ((central_trans (clamp .2 1 (- 1 (dotproduct (faceforward N I) (* -1 I))))))
    (* (- 1 (smoothstep 0 1 (- height noiseval))  central_trans))))

(defun shader (userparamters Color Opacity Normal)
  (shade (* Color Opacity) Normal))

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