File:Gjl-cmap-5-10-1-10-0.jpg

DescriptionGjl-cmap-5-10-1-10-0.jpg	A color map illustrating Visualising Complex Functions
Date	25 March 2008
Source	Own work
Author	Georg-Johann Lay
Permission (Reusing this file)	Public domainPublic domainfalsefalse I, the copyright holder of this work, release this work into the public domain. This applies worldwide. In some countries this may not be legally possible; if so: I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

Summary[edit]

The values indexed s (saturation) control the transition saturated colors→white (resp. gray scale), i.e. intermediate values → infinity.

The values indexed h (value/valenz) control the transition black→bright, i.e. zero → nonzero.

Parameter a controls where the transition takes place: a is just the radius of the circle dividing the two regions (dark/bright, saturated/gray, etc.)

Parameter b controls how sharp the transition is: b small = soft, b large = sharp.

The following images all show the range [-10,10]×[-10,10]${\displaystyle i}$ and use ${\displaystyle a_{s}=5}$ (radius of rainbow) and ${\displaystyle a_{v}=1}$ (radius of black disc).

Gallery[edit]

• 
  ${\displaystyle b_{s}=b_{v}=10}$
• 
  ${\displaystyle b_{s}=b_{v}=1}$
• 
  ${\displaystyle b_{s}=0.05,b_{v}=1/3}$
• 
  ${\displaystyle b_{s}=0.05,b_{v}=1/3}$
  Roles of S and V interchanged

See also[edit]

• Visualising Complex Functions