I need to project points from the 2-D plane to a 3-D unit sphere centered at (0,0,0).
The context is Complex Analysis. The goal will be to map any linear fractional map to the sphere. For now I need to understand how Matlab can achieve the more basic projection of a fractal onto the sphere and do the reverse. I know Matlab has a mapping toolbox (that I dont erally understand either) and that may be sufficient.
Im not asking for a step by step process. Just a general direction to what functions and methods might be useful. I hope this question isnt too broad.
The following code creates a fractal image with data stored in the map(i,j) matrix.
—————————————————————————————————————-
clear all
clc
clf
res = 0.05;
x = -2:res:2;
y = x’;
depth = 32;
grid = zeros(length(x),length(y));
map =zeros(length(x),length(y));
c = 0.30 + 0.5*1i;
for i = 1:length(x)
for j = 1:length(y)
grid(i,j) = x(i)+y(j)*1i;
end
end

for i = 1:length(x)
for j = 1:length(y)
for n = 1:depth
if abs(grid(i,j)) > 2
map(i,j) = n;
break
else
grid(i,j) = grid(i,j)^2 + c;
end
end
end
end
map(map==0) = depth ;
map;
image(map)
axis image
colormap(flipud(jet(depth)))
————————————————————————————–
The data stored in map(i,j) is what needs to be projected.

Thank you allI need to project points from the 2-D plane to a 3-D unit sphere centered at (0,0,0).
The context is Complex Analysis. The goal will be to map any linear fractional map to the sphere. For now I need to understand how Matlab can achieve the more basic projection of a fractal onto the sphere and do the reverse. I know Matlab has a mapping toolbox (that I dont erally understand either) and that may be sufficient.
Im not asking for a step by step process. Just a general direction to what functions and methods might be useful. I hope this question isnt too broad.
The following code creates a fractal image with data stored in the map(i,j) matrix.
—————————————————————————————————————-
clear all
clc
clf
res = 0.05;
x = -2:res:2;
y = x’;
depth = 32;
grid = zeros(length(x),length(y));
map =zeros(length(x),length(y));
c = 0.30 + 0.5*1i;
for i = 1:length(x)
for j = 1:length(y)
grid(i,j) = x(i)+y(j)*1i;
end
end

for i = 1:length(x)
for j = 1:length(y)
for n = 1:depth
if abs(grid(i,j)) > 2
map(i,j) = n;
break
else
grid(i,j) = grid(i,j)^2 + c;
end
end
end
end
map(map==0) = depth ;
map;
image(map)
axis image
colormap(flipud(jet(depth)))
————————————————————————————–
The data stored in map(i,j) is what needs to be projected.

Thank you all I need to project points from the 2-D plane to a 3-D unit sphere centered at (0,0,0).
The context is Complex Analysis. The goal will be to map any linear fractional map to the sphere. For now I need to understand how Matlab can achieve the more basic projection of a fractal onto the sphere and do the reverse. I know Matlab has a mapping toolbox (that I dont erally understand either) and that may be sufficient.
Im not asking for a step by step process. Just a general direction to what functions and methods might be useful. I hope this question isnt too broad.
The following code creates a fractal image with data stored in the map(i,j) matrix.
—————————————————————————————————————-
clear all
clc
clf
res = 0.05;
x = -2:res:2;
y = x’;
depth = 32;
grid = zeros(length(x),length(y));
map =zeros(length(x),length(y));
c = 0.30 + 0.5*1i;
for i = 1:length(x)
for j = 1:length(y)
grid(i,j) = x(i)+y(j)*1i;
end
end

for i = 1:length(x)
for j = 1:length(y)
for n = 1:depth
if abs(grid(i,j)) > 2
map(i,j) = n;
break
else
grid(i,j) = grid(i,j)^2 + c;
end
end
end
end
map(map==0) = depth ;
map;
image(map)
axis image
colormap(flipud(jet(depth)))
————————————————————————————–
The data stored in map(i,j) is what needs to be projected.

Thank you all fractal, stereographic projection, reimann sphere, fractional linear mapping MATLAB Answers — New Questions

​