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171<p class="navigation-index">[<a href="#fx">The Fx Special Effects Image Operator</a> &bull; <a href="#anatomy">The Anatomy of an Fx Expression</a>]</p>
172
173<h2><a name="fx"></a>The Fx Special Effects Image Operator</h2>
174<div class="doc-section">
175
176<p>Use the Fx special effects image operator to apply a mathematical expression to an image or image channels.  Use Fx to:</p>
177
178<ul>
179  <li>create canvases, gradients, mathematical colormaps</li>
180  <li>move color values between images and channels</li>
181  <li>translate, flip, mirror, rotate, scale, shear and generally distort images</li>
182  <li>merge or composite multiple images together</li>
183  <li>convolve or merge neighboring pixels together</li>
184  <li>generate image metrics or 'fingerprints'</li>
185</ul>
186
187<p>The expression can be simple:</p>
188
189<p class='crt'><span class="crtprompt"> $magick&gt; </span><span class='crtin'>convert -size 64x64 xc:black -channel blue -fx "1/2" fx_navy.png</span></p>
190<p>Here, we convert a black to a navy blue image:</p>
191
192<p class="image">
193  <a href="/images/black.png"><img src="/images/black.png" width="64" height="64" alt="black" /></a>
194  <img style="margin-top:22px; margin-bottom:22px;" src="/images/right.gif" width="20" height="20" alt="==>" />
195  <a href="/images/navy.png"><img src="/images/navy.png" width="64" height="64" alt="navy" /></a>
196</p>
197
198<p>Or the expression can be complex:</p>
199
200<p class='crt'><span class="crtprompt"> $magick&gt; </span><span class='crtin'>convert rose.jpg \  <br/>
201          -fx "(1.0/(1.0+exp(10.0*(0.5-u)))-0.006693)*1.0092503" \ <br/>
202          rose-sigmoidal.png</span></p>
203<p>This expression results in a high contrast version of the image:</p>
204
205<p class="image">
206  <a href="/images/rose.jpg"><img src="/images/rose.jpg" width="70" height="46" alt="rose" /></a>
207  <img style="margin-top:13px; margin-bottom:13px;" src="/images/right.gif" width="20" height="20" alt="==>" />
208  <a href="/images/rose-sigmoidal.png"><img src="/images/rose-sigmoidal.png" width="70" height="46" alt="rose-sigmoidal" /></a>
209</p>
210
211<p>The expression can include variable assignments.  Assignments, in most cases, reduce the complexity of an expression and permit some operations that might not be possible any other way.  For example, lets create a radial gradient:</p>
212
213<p class='crt'><span class="crtprompt"> $magick&gt; </span><span class='crtin'>convert -size 70x70 xc: \  <br/>
214          -fx "Xi=i-w/2; Yj=j-h/2; 1.2*(0.5-hypot(Xi,Yj)/70.0)+0.5" \ <br/>
215          radial-gradient.png</span></p>
216<p>The command above returns this image:</p>
217
218<p class="image">
219  <a href="/images/radial-gradient.png"><img src="/images/radial-gradient.png" width="70" height="70" alt="radial-gradient" /></a>
220</p>
221<p>See <a href="http://www.imagemagick.org/Usage/transform/index.html#fx">Using FX, The Special Effects Image Operator</a> for more examples.</p>
222
223<p>The next section discusses the Fx expression language.</p>
224
225</div>
226
227<h2><a name="anatomy"></a>The Anatomy of an Fx Expression</h2>
228<div class="doc-section">
229
230<h3>The Fx Expression Language</h3>
231<div class="doc-section">
232
233<p>The formal Fx expression language is defined here:</p>
234
235<dl class="doc">
236  <dt class="doc"> numbers:</dt>
237  	<dd> integer, floating point, or scientfic notation (+/- required, e.g. 3.81469e-06)</dd>
238  <dt class="doc"> constants: </dt>
239    <dd> e, Epsilon, QuantumRange, QuantumScale, Opaque, Pi, Transparent</dd>
240  <dt class="doc"> Fx operators (in order of precedence): </dt>
241     <dd> ^ (power), *, /, % (modulo), +, -,
242     &lt;&lt;, &gt;&gt;, &lt;, &lt;=, &gt;, &gt;=, ==, !=,
243     &amp; (bitwise AND),   | (bitwise OR),
244     &amp;&amp; (logical AND),  || (logical OR),
245     ~ (logical NOT),  ?: (ternary conditional)</dd>
246  <dt class="doc"> math functions: </dt>
247     <dd> abs(), acos(), airy(), alt(), asin(), atan(), atan2(), ceil(), cos(), cosh(), debug(), exp(), floor(),
248     hypot(), int(), j0(), j1(), jinc(), ln(), log(), logtwo(), max(), min(), mod(), pow(), rand(), round(),
249     sign(), sin(), sinc(), sinh(), sqrt(), tan(), tanh(), trunc()</dd>
250  <dt class="doc"> channel functions: </dt>
251    <dd> channel(r,g,b,a), channel(c,m,y,k,a)</dd>
252  <dt class="doc"> color names:</dt>
253    <dd> red, cyan, black, etc.</dd>
254  <dt class="doc"> color functions:</dt>
255    <dd> rgb(), rgba(), cmyk(), cmyka(), hsl(), hsla()</dd>
256  <dt class="doc"> color hex values:</dt>
257    <dd> #ccc, #cbfed0, #b9e1cc00</dd>
258  <dt class="doc"> symbols:</dt>
259     <dd style="white-space:pre">
260     s = current image in sequence
261     t = scene number of current image in sequence
262     u = first image in sequence
263     v = second image in sequence
264     n = number of images in sequence
265
266     i = column offset
267     j = row offset
268     p = pixel to use (absolute or relative to current pixel)
269
270     w = width of this image
271     h = height of this image
272     z = channel depth
273
274     r = red value (from RGBA), of a specific or current pixel
275     g = green    ''
276     b = blue     ''
277     a = alpha    ''
278     o = opacity  ''
279
280     c = cyan value of CMYK color of pixel
281     y = yellow   ''
282     m = magenta  ''
283     k = black    ''
284
285     intensity = pixel intensity
286
287     hue = pixel hue
288     saturation = pixel saturation
289     lightness = pixel lightness
290     luminance = pixel luminance
291
292     page.width = page width
293     page.height = page height
294     page.x = page x offset
295     page.y = page y offset
296
297     resolution.x = x resolution
298     resolution.y = y resolution
299
300     depth = image depth
301     minima = image minima
302     maxima = image maxima
303     mean = image mean
304     standard_deviation = image standard deviation
305     kurtosis = image kurtosis
306     skewness = image skewness
307       (add a channel specifier to compute a statistic for that channel, e.g. depth.r)
308     </dd>
309</dl>
310
311</div>
312
313<h3>The Fx Expression</h3>
314<div class="doc-section">
315
316<p>An Fx expression may include any combination of the following:</p>
317<ul>
318<li> <em>x</em> <kbd>^</kbd> <em>y</em>:  exponentiation (<em>x<sup>y</sup></em>)</li>
319<li> <kbd>(</kbd> ... <kbd>)</kbd>:  grouping</li>
320<li> <em>x</em> <kbd>*</kbd> <em>y</em>:  multiplication (the asterisk <kbd>*</kbd> is optional, for example, <kbd>2u</kbd> or <kbd>2(x+y)</kbd> are acceptable)</li>
321<li> <em>x</em> <kbd>/</kbd> <em>y</em>:  division</li>
322<li> <em>x</em> <kbd>%</kbd> <em>y</em>:  modulo</li>
323<li> <em>x</em> <kbd>+</kbd> <em>y</em>:  addition</li>
324<li> <em>x</em> <kbd>-</kbd> <em>y</em>:  subtraction</li>
325<li> <em>x</em> <kbd>&lt;&lt;</kbd> <em>y</em>:  left shift</li>
326<li> <em>x</em> <kbd>&gt;&gt;</kbd> <em>y</em>:  right shift</li>
327<li> <em>x</em> <kbd>&lt;</kbd> <em>y</em>:  boolean relation, return value 1.0 if <em>x</em> &lt; <em>y</em>,  otherwise 0.0</li>
328<li> <em>x</em> <kbd>&lt;=</kbd> <em>y</em>:  boolean relation, return value 1.0 if <em>x</em> &lt;= <em>y</em>,  otherwise 0.0</li>
329<li> <em>x</em> <kbd>&gt;</kbd> <em>y</em>:  boolean relation, return value 1.0 if <em>x</em> &gt; <em>y</em>,  otherwise 0.0</li>
330<li> <em>x</em> <kbd>&gt;=</kbd> <em>y</em>:  boolean relation, return value 1.0 if <em>x</em> &gt;= <em>y</em>,  otherwise 0.0</li>
331<li> <em>x</em> <kbd>==</kbd> <em>y</em>:  boolean relation, return value 1.0 if <em>x </em>==<em> y</em>, otherwise 0.0</li>
332<li> <em>x</em> <kbd>!=</kbd> <em>y</em>:  boolean relation, return value 1.0 if <em>x </em>!=<em> y</em>, otherwise 0.0</li>
333<li> <em>x</em> <kbd>&amp;</kbd> <em>y</em>:  binary AND</li>
334<li> <em>x</em> <kbd>|</kbd> <em>y</em>:  binary OR</li>
335<li> <em>x</em> <kbd>&amp;&amp;</kbd> <em>y</em>:  logical AND connective, return value 1.0 if <em>x</em> &gt; 0 and <em>y</em> &gt; 0,  otherwise 0.0</li>
336<li> <em>x</em> <kbd>||</kbd> <em>y</em>:  logical OR connective (inclusive), return value 1.0 if <em>x</em> &gt; 0 or <em>y</em> &gt; 0 (or both),  otherwise 0.0</li>
337<li> <kbd>~</kbd><em>x</em>:  logical NOT operator, return value 1.0 if <em>not</em> <em>x</em> &gt; 0,  otherwise 0.0</li>
338<li> <kbd>+</kbd><em>x</em>:  unary plus, return 1.0*value</li>
339<li> <kbd>-</kbd><em>x</em>:  unary minus, return -1.0*value</li>
340<li> <em>x</em> <kbd>?</kbd> <em>y</em> : <em>z</em>: ternary conditional expression, return value <em>y</em> if <em>x</em> != 0, otherwise <em>z</em>; only one ternary conditional permitted per statement</li>
341<li> <em>x</em> <kbd>=</kbd> <em>y</em>: assignment; assignment variables are restricted to letter combinations only (e.g. Xi not X1)</li>
342<li> <em>x</em> <kbd>;</kbd> <em>y</em>: statement separator </li>
343<li> <kbd>pi</kbd>:  constant (3.141659...)</li>
344<li> <kbd>e</kbd>:  constant (2.71828...)</li>
345<li> <kbd>QuantumRange</kbd>:  constant maximum pixel value (255 for Q8, 65535 for Q16)</li>
346<li> <kbd>QuantumScale</kbd>:  constant 1.0/<kbd>QuantumRange</kbd></li>
347<li> <kbd>intensity</kbd>:  pixel intensity; equivalent to 0.299*red+0.587*green+0.114*blue</li>
348<li> <kbd>hue</kbd>:  pixel hue</li>
349<li> <kbd>saturation</kbd>:  pixel saturation</li>
350<li> <kbd>lightness</kbd>:  pixel lightness; equivalent to 0.5*max(red,green,blue) + 0.5*min(red,green,blue)</li>
351<li> <kbd>luminance</kbd>:  pixel luminance; equivalent to 0.2126*red + 0.7152*green + 0.0722*blue</li>
352<li> <kbd>red, green, blue</kbd>, etc.:  color names</li>
353<li> <kbd>#ccc, #cbfed0, #b9e1cc00</kbd>, etc.:  color hex values</li>
354<li> <kbd>rgb(), rgba(), cmyk(), cmyka(), hsl(), hsla()</kbd>:  color functions</li>
355<li> <kbd>s, t, u, v, n, i, j, w, h, z, r, g, b, a, o, c, y, m, k</kbd>:  symbols</li>
356<li> <kbd>abs(</kbd><em>x</em><kbd>)</kbd>:  absolute value function</li>
357<li> <kbd>acos(</kbd><em>x</em><kbd>)</kbd>:  arc cosine function</li>
358<li> <kbd>airy(</kbd><em>x</em><kbd>)</kbd>:  Airy function (max=1, min=0); <kbd>airy(</kbd><em>x</em><kbd>)</kbd>=<kbd>[jinc(</kbd><em>x</em><kbd>)]<sup>2</sup></kbd>=<kbd>[2*j1(</kbd><em>pi*x</em><kbd>)/(</kbd><em>pi*x</em><kbd>)]<sup>2</sup></kbd></li>
359<li> <kbd>alt(</kbd><em>x</em><kbd>)</kbd>:  sign alternation function (return 1.0 if <kbd>int(</kbd><em>x</em><kbd>)</kbd> is even, -1.0 if <kbd>int(</kbd><em>x</em><kbd>)</kbd> is odd)</li>
360<li> <kbd>asin(</kbd><em>x</em><kbd>)</kbd>:  arc sine function</li>
361<li> <kbd>atan(</kbd><em>x</em><kbd>)</kbd>:  arc tangent function</li>
362<li> <kbd>atan2(</kbd><em>y</em>,<em>x</em><kbd>)</kbd>:  arc tangent function of two variables</li>
363<li> <kbd>ceil(</kbd><em>x</em><kbd>)</kbd>: smallest integral value not less than argument</li>
364<li> <kbd>channel(</kbd><em>r</em>,<em>g</em>,<em>b</em>,<em>a</em><kbd>)</kbd>: select numeric argument based on current channel</li>
365<li> <kbd>channel(</kbd><em>c</em>,<em>m</em>,<em>y</em>,<em>k</em>,<em>a</em><kbd>)</kbd>: select numeric argument based on current channel</li>
366<li> <kbd>cos(</kbd><em>x</em><kbd>)</kbd>:  cosine function</li>
367<li> <kbd>cosh(</kbd><em>x</em><kbd>)</kbd>:  hyperbolic cosine function</li>
368<li> <kbd>debug(</kbd><em>x</em><kbd>)</kbd>:  print <em>x</em> (useful for debugging your expression)</li>
369<li> <kbd>exp(</kbd><em>x</em><kbd>)</kbd>:  natural exponential function (<em>e<sup>x</sup></em>)</li>
370<li> <kbd>floor(</kbd><em>x</em><kbd>)</kbd>:  largest integral value not greater than argument</li>
371<li> <kbd>hypot(</kbd><em>x</em>,<em>y</em><kbd>)</kbd>:  the square root of x<sup>2</sup>+y<sup>2</sup></li>
372<li> <kbd>int(</kbd><em>x</em><kbd>)</kbd>:  greatest integer function (return greatest integer less than or equal to <em>x</em>)</li>
373<li> <kbd>j0(</kbd><em>x</em><kbd>)</kbd>:  Bessel functions of <em>x</em> of the first kind of order 0</li>
374<li> <kbd>j1(</kbd><em>x</em><kbd>)</kbd>:  Bessel functions of <em>x</em> of the first kind of order 1</li>
375<li> <kbd>jinc(</kbd><em>x</em><kbd>)</kbd>:  jinc function (max=1, min=-0.1323); <kbd>jinc(</kbd><em>x</em><kbd>)</kbd>=<kbd>2*j1(</kbd><em>pi*x</em><kbd>)/(</kbd><em>pi*x</em><kbd>)</kbd></li>
376<li> <kbd>ln(</kbd><em>x</em><kbd>)</kbd>:  natural logarithm function</li>
377<li> <kbd>log(</kbd><em>x</em><kbd>)</kbd>:  logarithm base 10</li>
378<li> <kbd>logtwo(</kbd><em>x</em><kbd>)</kbd>:  logarithm base 2</li>
379<li> <kbd>ln(</kbd><em>x</em><kbd>)</kbd>:  natural logarithm</li>
380<li> <kbd>max(</kbd><em>x</em>, <em>y</em><kbd>)</kbd>:  maximum of <em>x</em> and <em>y</em></li>
381<li> <kbd>min(</kbd><em>x</em>, <em>y</em><kbd>)</kbd>:  minimum of <em>x</em> and <em>y</em></li>
382<li> <kbd>mod(</kbd><em>x</em>, <em>y</em><kbd>)</kbd>:  floating-point remainder function</li>
383<li> <kbd>pow(</kbd><em>x</em>,<em>y</em><kbd>)</kbd>:  power function (<em>x<sup>y</sup></em>)</li>
384<li> <kbd>rand()</kbd>:  value uniformly distributed over the interval [0.0, 1.0) with a 2 to the 128th-1 period</li>
385<li> <kbd>round()</kbd>:  round to integral value, regardless of rounding direction</li>
386<li> <kbd>sign(</kbd><em>x</em><kbd>)</kbd>:  return -1.0 if <em>x</em> is less than 0.0 otherwise 1.0</li>
387<li> <kbd>sin(</kbd><em>x</em><kbd>)</kbd>:  sine function</li>
388<li> <kbd>sinc(</kbd><em>x</em><kbd>)</kbd>:  sinc function (max=1, min=-0.21); <kbd>sinc(</kbd><em>x</em><kbd>)</kbd>=<kbd>sin(</kbd><em>pi*x</em><kbd>)/(</kbd><em>pi*x</em><kbd>)</kbd></li>
389<li> <kbd>sinh(</kbd><em>x</em><kbd>)</kbd>:  hyperbolic sine function</li>
390<li> <kbd>sqrt(</kbd><em>x</em><kbd>)</kbd>:  square root function</li>
391<li> <kbd>tan(</kbd><em>x</em><kbd>)</kbd>:  tangent function</li>
392<li> <kbd>tanh(</kbd><em>x</em><kbd>)</kbd>:  hyperbolic tangent function</li>
393<li> <kbd>trunc(</kbd><em>x</em><kbd>)</kbd>:  round to integer, towards zero</li>
394</ul>
395
396<p>The expression semantics include these rules:</p>
397
398<ul>
399<li>symbols are case insensitive</li>
400<li>only one ternary conditional (e.g. x ? y : z) per statement</li>
401<li>statements are assignments or the final expression to return</li>
402<li>an assignment starts a statement, it is not an operator</li>
403<li>assignments to built-ins do not throw an exception and have no effect;  e.g. <kbd>r=3.0; r</kbd> returns the pixel red color value, not 3.0</li>
404</ul>
405
406</div>
407
408<h3>Source Images</h3>
409<div class="doc-section">
410
411<p>The symbols <kbd>u</kbd> and <kbd>v</kbd> refer to the first and second images, respectively, in the current image sequence.  Refer to a particular image in a sequence by appending its index to any image reference (usually <kbd>u</kbd>), with a zero index for the beginning of the sequence. A negative index counts from the end.  For example, <kbd>u[0]</kbd> is the first image in the sequence, <kbd>u[2]</kbd> is the third, <kbd>u[-1]</kbd> is the last image, and <kbd>u[t]</kbd> is the current image. The current image can also be referenced by <kbd>s</kbd>. If the sequence number exceeds the length of the sequence, the count is wrapped. Thus in a 3-image sequence,  <kbd>u[-1]</kbd>, <kbd>u[2]</kbd>, and <kbd>u[5]</kbd> all refer to the same (third) image.</p>
412
413<p>As an example, we form an image by averaging the first image and third images:</p>
414
415<p class='crt'><span class="crtprompt"> $magick&gt; </span><span class='crtin'>convert image1.jpg image2.jpg image3.jpg -fx "(u+u[2])/2.0" image.jpg</span></p>
416<p>By default, the image to which <kbd>p</kbd>, <kbd>r</kbd>, <kbd>g</kbd>, <kbd>b</kbd>, <kbd>a</kbd>, etc., are applied is the first image <kbd>u</kbd> in the image list, which may also be referenced using <kbd>s</kbd>. </p>
417
418<p>It is important to note the special role played by the first image. This is the only image in the image sequence that is modified, other images are used only for their data. As an illustrative example, consider the following, and note that the setting <a href="/www/command-line-options.html#channel">-channel red</a> instructs <a href="/www/command-line-options.html#fx">-fx</a> to modify only the red channel; nothing in the green or blue channels will change. It is instructive to ponder why the result is not symmetric.</p>
419
420<p class='crt'><span class="crtprompt"> $magick&gt; </span><span class='crtin'>convert -channel red logo: -flop logo: -resize "20%"  -fx "(u+v)/2" image.jpg</span></p>
421<div class="image">
422<p>
423  <a href="/images/logo-sm-flop.png"><img src="/images/logo-sm-flop.png" width="128" height="96" alt="logo-sm-flop.png" /></a>
424  <a href="/images/logo-sm.png"><img src="/images/logo-sm.png" width="128" height="96" alt="logo-sm.png" /></a>
425<img style="margin-top:38px; margin-bottom:38px;" src="/images/right.gif" width="20" height="20" alt="==>" />
426  <a href="/images/logo-sm-fx.png"><img src="/images/logo-sm-fx.png" width="128" height="96" alt="logo-sm-fx.png" /></a>
427</p>
428</div>
429
430
431</div>
432
433<h3>Accessing Pixels</h3>
434<div class="doc-section">
435
436<p>All color values are normalized to the range of 0.0 to 1.0.  The alpha channel ranges from 0.0 (fully transparent) to 1.0 (fully opaque).</p>
437
438<p>The pixels are processed one at a time, but a different pixel of an image can be specified using a pixel index represented by <kbd>p</kbd>. For example,</p>
439
440<pre class="text">
441   p[-1].g      green value of pixel to the immediate left of the current pixel
442   p[-1,-1].r   red value of the pixel diagonally left and up from current pixel
443</pre>
444
445<p>To specify an absolute position, use braces, rather than brackets.</p>
446
447<pre class="text">
448  p{0,0}.r   red value of the pixel in the upper left corner of the image
449  p{12,34}.b   blue pixel value at column number 12, row 34 of the image
450</pre>
451
452<p>Integer values of the position retrieve the color of the pixel referenced, while non-integer position values return a blended color according to the current <a href="/www/command-line-options.html#interpolate">-interpolate</a> setting.</p>
453
454<p>A position outside the boundary of the image retrieves a value dictated by the <a href="/www/command-line-options.html#virtual-pixel">-virtual-pixel</a> option setting.</p>
455
456</div>
457
458<h3>Apply an Expression to Select Image Channels</h3>
459<div class="doc-section">
460
461<p>Use the <a href="/www/command-line-options.html#channel">-channel</a> setting to specify the output channel of the result. If no output channel is given, the result is set over all channels except the opacity channel. For example, to replace the red channel of <kbd>alpha.png</kbd> with the average of the green channels from the images <kbd>alpha.png</kbd> and <kbd>beta.png</kbd>, use:</p>
462
463<p class='crt'><span class="crtprompt"> $magick&gt; </span><span class='crtin'>convert alpha.png beta.png -channel red -fx "(u.g+v.g)/2" gamma.png</span></p>
464</div>
465
466<h3>Results</h3>
467<div class="doc-section">
468
469<p>The <a href="/www/command-line-options.html#fx">-fx</a> operator evaluates the given expression for each channel (set by <a href="/www/command-line-options.html#channel">-channel</a>) of each pixel in the first image (<kbd>u</kbd>) in the sequence. The computed values are temporarily stored in a copy (clone) of that first image until all the pixels have been processed, after which this single new image replaces the list of images in the current image sequence.  As such, in the previous example the updated version of <kbd>alpha.png</kbd> replaces both of the original images, <kbd>alpha.png</kbd> and <kbd>beta.png</kbd>, before being saved as <kbd>gamma.png</kbd>.</p>
470
471<p>The current image <kbd>s</kbd> is set to the first image in the sequence (<kbd>u</kbd>), and <kbd>t</kbd> to its index, 0.  The symbols <kbd>i</kbd> and <kbd>j</kbd> reference the current pixel being processed.</p>
472
473
474<p>For use with <a href="/www/command-line-options.html#format_identify_">-format</a>, the value-escape <kbd>%[fx: ]</kbd> is evaluated just once for each image in the current image sequence. As each image in the sequence is being evaluated, <kbd>s</kbd> and <kbd>t</kbd> successively refer to the current image and its index, while <kbd>i</kbd> and <kbd>j</kbd> are set to zero, and the current channel set to red (<a href="/www/command-line-options.html#channel">-channel</a> is ignored). An example:</p>
475
476<p class='crt'><span class="crtprompt"> $magick&gt; </span><span class='crtin'>convert  xc:'rgb(25%,50%,75%)' rose: -colorspace rgb  \ <br/>
477  -format 'Red channel of NW corner of image # %[fx:t] is %[fx: s]' info:</span><span class='crtout'>Red channel of NW corner of image # 0 is 0.250004 <br/>
478  Red channel of NW corner of image # 1 is 0.188235</span></p>
479<p>Use <kbd>%[fxc: ]</kbd> if your expression is a constant (e.g. <kbd>%[fxc:page.x/2]</kbd>.  The result is cached and the cached result returned rather than evaluating the expression each time.</p>
480
481<p>The color-escape <kbd>%[pixel: ]</kbd> is evaluated once per image and per color channel in that image (<a href="/www/command-line-options.html#channel">-channel</a> is ignored), The values generated are then converted into a color string (a named color or hex color value).  The symbols <kbd>i</kbd> and <kbd>j</kbd> are set to zero, and <kbd>s</kbd> and <kbd>t</kbd> refer to each successively current image and index.</p>
482
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