G.Projector is a wonderful tool made by the NASA capable of reprojecting an equirectangular into pretty much every type of projection there is, below is an example of a fractal map and some of the weirdest projections I have seen
Equirectangular
Untitled-1.jpg
Gnomonic Cubed Sphere
gnomonic cubes sphere.png
Gringorten
gringorten.png
Bonne
bonne.png
It can be downloaded for free from http://www.giss.nasa.gov/tools/gprojector
Here is a list of available projections:
Adams Orthembadic: See Quartic Authalic.
Aitoff: Polyconic, equally spaced parallels.
Aitoff-Wagner: See Wagner IX.
Albers Equal-Area Conic: Conic.
Apian I: See Ortelius Oval.
Apian II: Pseudocylindric, equally spaced parallels, elliptical meridians.
Azimuthal Equal-Area: Azimuthal, equal-area
Azimuthal Equidistant: Azimuthal.
Babinet: See Mollweide.
Bacon Globular: Pseudocylindric.
Baker Dinomic: Fusion; joins Mercator and ??? at 45°.
Behrmann: See Cylindrical Equal-Area and apply ϕts=30°.
Boggs Eumorphic: Pseudocylindric, equal-area; Often shown interrupted.
Bonne: Pseudoconic, equal-area.
Braun Perspective: Cylindric.
Braun Stereographic: Cylindric.
Canters: See Canters Polyconic 1989 f9.
Canters Polyconic 1989 f9: Polyconic, low-error.
Canters Pseudocylindric 2002 f5.18: Pseudocylindric, low-error, pole line.
Canters Pseudocylindric 2002 f5.19: Pseudocylindric, low-error, pole line.
Canters Pseudocylindric 2002 f5.20: Pseudocylindric, low-error, pole line.
Canters Pseudocylindric 2002 f5.23: Pseudocylindric, low-error, pointed pole.
Cordiform: See Bonne and apply ϕ0=90°.
Craster Parabolic: See Parabolic.
Cylindrical Equal-Area: Cylindric, equal-area.
Cylindrical Equidistant: See Equirectangular.
Denoyer Semi-Elliptical: Pseudocylindric.
Eckert III: Pseudocylindric, equally spaced parallels, elliptical meridians, pole line.
Eckert IV: Pseudocylindric, equal-area, elliptical meridians, pole line.
Eckert V: Pseudocylindric, equally spaced parallels, sinusoidal meridians, pole line.
Eckert VI: Pseudocylindric, equal-area, sinusoidal meridians, pole line.
Eckert-Greifendorff: Polyconic, equal-area.
Equidistant Conic: Conic, equally spaced parallels.
Equirectangular: Cylindric, equidistant.
Érdi-Krausz: Fusion.
Fahey: Pseudocylindric.
Foucaut: Pseudocylindric.
Fournier Globular I: Polyconic.
Gall Isographic: See Equirectangular and apply ϕts=45°.
Gall Orthographic: See Cylindrical Equal-Area and apply ϕts=45°.
Gall Stereographic: Cylindric.
Gall-Peters: See Cylindrical Equal-Area and apply ϕts=45°.
Ginsburg VIII: Pseudocylindric.
Goode Homolosine: Fusion; joins Sinusoidal and Mollweide at 40°44'. Often shown interrupted.
Gott Equal-Area Elliptical: Equal-Area.
Gott-Mugnolo Azimuthal: Azimuthal.
Gnomonic: Azimuthal.
Gnomonic Cubed Sphere.
Gringorten: Equal-Area.
Hammer: Polyconic, equal-area.
Hammer-Aitoff: See Hammer.
Hammer-Wagner: See Wagner VII.
Hill Eucyclic: Polyconic, equal-area. Note: identical to Eckert IV for K=∞.
Hölzel: Pseudocylindric.
Homalographic: See Mollweide.
Homolographic: See Mollweide.
Kavraisky V: Pseudocylindric, equal-area.
Kavraisky VI: See Wagner I.
Kavraisky VII: Pseudocylindric, equally spaced parallels, elliptical meridians, pole line.
Lambert Azimuthal Equal-Area: See Azimuthal Equal-Area.
Lambert Conformal Conic: Conic.
Lambert Cylindrical Equal-Area: See Cylindrical Equal-Area and apply ϕts=0°.
Larrivée:
Maurer SNo. 173: See Hill Eucyclic and apply K=0.
Mayr: Pseudocylindric, equal-area.
McBryde P3: Fusion; joins Parabolic and M.T. Flat-Polar Parabolic at 49°20'. Often shown interrupted.
McBryde Q3: Fusion; joins Quartic Authalic and M.T. Flat-Polar Quartic Authalic at 52°9'. Often shown interrupted
McBryde S2: Fusion; joins Sinusoidal and Eckert VI at 49°16'. Often shown interrupted
McBryde S3: Fusion; joins Sinusoidal and ??? at 55°51'. Often shown interrupted.
McBryde-Thomas Flat-Polar Parabolic: Pseudocylindric, equal-area, parabolic meridians, pole line. Often shown interrupted.
McBryde-Thomas Flat-Polar Quartic: Pseudocylindric, equal-area, quartic meridians, pole line. Often shown interrupted.
McBryde-Thomas Flat-Polar Sinusoidal: Pseudocylindric, equal-area, sinusoidal meridians, pole line. Often shown interrupted.
McBryde-Thomas Sine #1: Pseudocylindric.
Mercator: Cylindric.
Miller Cylindric: Cylindric.
Modified Gall: Pseudocylindric.
Mollweide: Pseudocylindric, equal-area, elliptical meridians. Often shown interrupted.
Nell: Pseudocylindric, pole line.
Nell-Hammer: Pseudocylindric, equal-area, pole line.
Ortelius Oval: Pseudocylindric, equally spaced parallels, circular meridians, pole line.
Orthographic: Azimuthal, perspective view.
Orthophanic: See Robinson.
Oxford Atlas: See Modified Gall.
Parabolic: Pseudocylindric, equal-area, parabolic meridians.
Pavlov: Cylindric.
Peters: See Cylindrical Equal-Area and apply ϕts=45°.
Plate Carrée: See Equirectangular and apply ϕts=0°.
Putniņš P1: Pseudocylindric, equally spaced parallels, elliptical meridians.
Putniņš P1': See Wagner VI.
Putniņš P2: Pseudocylindric, elliptical meridians.
Putniņš P2': See Wagner IV.
Putniņš P3: Pseudocylindric, equally spaced parallels, parabolic meridians.
Putniņš P3': Pseudocylindric, equally spaced parallels, parabolic meridians, pole line.
Putniņš P4: See Parabolic.
Putniņš P4': Pseudocylindric, equal-area, parabolic meridians, pole line.
Putniņš P5: Pseudocylindric.
Putniņš P5': Pseudocylindric, pole line.
Putniņš P6: Pseudocylindric, hyperbolic meridians.
Putniņš P6': Pseudocylindric, hyperbolic meridians, pole line.
Quartic-Authalic: Pseudocylindric.
Raisz Armadillo: Orthoapsidal.
Raisz Half Ellipsoidal: Orthoapsidal
Robinson: Pseudocylindric, pole line.
Sanson-Flamsteed: See Sinusoidal.
Sinusoidal: Pseudocylindric, equal-area, sinusoidal meridians. Often shown interrupted.
Stereographic: Azimuthal.
Times Atlas: Pseudocylindric.
Tobler G1: Pseudocylindric, equal-area.
TsNIIGAiK: See Ginsburg VIII.
Urmayev Sinusoidal: Pseudocylindric, equal-area, sinusoidal meridians, pole line except for b=1 case. Note: identical to Wagner I if b=0.866; identical to Cylindrical Equal-Area for ϕts=28° if b=0; compressed horizontally from classic Sinusoidal if b=1.
Van Der Grinten I: Polyconic, circular meridians, parallels.
Vertical Perspective: Azimuthal, perspective view. Note: identical to Orthographic if P=∞.
Wagner I: Pseudocylindric, equal-area, sinusoidal meridians, pole line.
Wagner II: Pseudocylindric, sinusoidal meridians, pole line.
Wagner III: Pseudocylindric, equally spaced parallels, sinusoidal meridians, pole line.
Wagner IV: Pseudocylindric, equal-area, elliptical meridians, pole line.
Wagner V: Pseudocylindric, elliptical meridians, pole line.
Wagner VI: Pseudocylindric, equally spaced parallels, elliptical meridians, pole line.
Wagner VII: Polyconic, equal-area, pole line.
Wagner VIII: Polyconic, pole line.
Wagner IX: Polyconic, equally spaced parallels, pole line.
Werenskiold I: See Putniņš P4'.
Werenskiold II: See Wagner I.
Werenskiold III: See Wagner IV.
Werner II: See Bonne and apply ϕ0=90°.
Winkel I: Pseudocylindric, equally spaced parallels, sinusoidal meridians, pole line.
Winkel II: Pseudocylindric, equally spaced parallels, elliptical meridians, pole line.
Winkel Tripel: Polyconic, equally spaced parallels, pole line.